define statistics assignment

Introduction to Statistics

(15 reviews)

David Lane, Rice University

Publisher: David Lane

Language: English

Formats Available

Conditions of use.

Learn more about reviews.

Reviewed by Terri Torres, professor, Oregon Institute of Technology on 8/17/23

This author covers all the topics that would be covered in an introductory statistics course plus some. I could imagine using it for two courses at my university, which is on the quarter system. I would rather have the problem of too many topics... read more

Comprehensiveness rating: 5 see less

Content Accuracy rating: 5

Yes, Lane is both thorough and accurate.

Relevance/Longevity rating: 5

What is covered is what is usually covered in an introductory statistics book. The only topic I may, given sufficient time, cover is bootstrapping.

Clarity rating: 5

The book is clear and well-written. For the trickier topics, simulations are included to help with understanding.

Consistency rating: 5

All is organized in a way that is consistent with the previous topic.

Modularity rating: 5

The text is organized in a way that easily enables navigation.

Organization/Structure/Flow rating: 5

The text is organized like most statistics texts.

Interface rating: 5

Easy navigation.

Grammatical Errors rating: 5

I didn't see any grammatical errors.

Cultural Relevance rating: 5

Nothing is included that is culturally insensitive.

The videos that accompany this text are short and easy to watch and understand. Videos should be short enough to teach, but not so long that they are tiresome. This text includes almost everything: videos, simulations, case studies---all nicely organized in one spot. In addition, Lane has promised to send an instructor's manual and slide deck.

Reviewed by Professor Sandberg, Professor, Framingham State University on 6/29/21

This text covers all the usual topics in an Introduction to Statistics for college students. In addition, it has some additional topics that are useful. read more

This text covers all the usual topics in an Introduction to Statistics for college students. In addition, it has some additional topics that are useful.

I did not find any errors.

Some of the examples are dated. And the frequent use of male/female examples need updating in terms of current gender splits.

I found it was easy to read and understand and I expect that students would also find the writing clear and the explanations accessible.

Even with different authors of chapter, the writing is consistent.

The text is well organized into sections making it easy to assign individual topics and sections.

The topics are presented in the usual order. Regression comes later in the text but there is a difference of opinions about whether to present it early with descriptive statistics for bivariate data or later with inferential statistics.

I had no problem navigating the text online.

The writing is grammatical correct.

I saw no issues that would be offensive.

I did like this text. It seems like it would be a good choice for most introductory statistics courses. I liked that the Monty Hall problem was included in the probability section. The author offers to provide an instructor's manual, PowerPoint slides and additional questions. These additional resources are very helpful and not always available with online OER texts.

Reviewed by Emilio Vazquez, Associate Professor, Trine University on 4/23/21

This appears to be an excellent textbook for an Introductory Course in Statistics. It covers subjects in enough depth to fulfill the needs of a beginner in Statistics work yet is not so complex as to be overwhelming. read more

I found no errors in their discussions. Did not work out all of the questions and answers but my sampling did not reveal any errors.

Some of the examples may need updating depending on the times but the examples are still relevant at this time.

This is a Statistics text so a little dry. I found that the derivation of some of the formulas was not explained. However the background is there to allow the instructor to derive these in class if desired.

The text is consistent throughout using the same verbiage in various sections.

The text dose lend itself to reasonable reading assignments. For example the chapter (Chapter 3) on Summarizing Distributions covers Central Tendency and its associated components in an easy 20 pages with Measures of Variability making up most of the rest of the chapter and covering approximately another 20 pages. Exercises are available at the end of each chapter making it easy for the instructor to assign reading and exercises to be discussed in class.

The textbook flows easily from Descriptive to Inferential Statistics with chapters on Sampling and Estimation preceding chapters on hypothesis testing

I had no problems with navigation

All textbooks have a few errors but certainly nothing glaring or making text difficult

I saw no issues and I am part of a cultural minority in the US

Overall I found this to be a excellent in-depth overview of Statistical Theory, Concepts and Analysis. The length of the textbook appears to be more than adequate for a one-semester course in Introduction to Statistics. As I no longer teach a full statistics course but simply a few lectures as part of our Research Curriculum, I am recommending this book to my students as a good reference. Especially as it is available on-line and in Open Access.

Reviewed by Audrey Hickert, Assistant Professor, Southern Illinois University Carbondale on 3/29/21

All of the major topics of an introductory level statistics course for social science are covered. Background areas include levels of measurement and research design basics. Descriptive statistics include all major measures of central tendency and dispersion/variation. Building blocks for inferential statistics include sampling distributions, the standard normal curve (z scores), and hypothesis testing sections. Inferential statistics include how to calculate confidence intervals, as well as conduct tests of one-sample tests of the population mean (Z- and t-tests), two-sample tests of the difference in population means (Z- and t-tests), chi square test of independence, correlation, and regression. Doesn’t include full probability distribution tables (e.g., t or Z), but those can be easily found online in many places.

I did not find any errors or issues of inaccuracy. When a particular method or practice is debated in the field, the authors acknowledge it (and provide citations in some circumstances).

Relevance/Longevity rating: 4

Basic statistics are standard, so the core information will remain relevant in perpetuity. Some of the examples are dated (e.g., salaries from 1999), but not problematic.

Clarity rating: 4

All of the key terms, formulas, and logic for statistical tests are clearly explained. The book sometimes uses different notation than other entry-level books. For example, the variance formula uses "M" for mean, rather than x-bar.

The explanations are consistent and build from and relate to corresponding sections that are listed in each unit.

Modularity is a strength of this text in both the PDF and interactive online format. Students can easily navigate to the necessary sections and each starts with a “Prerequisites” list of other sections in the book for those who need the additional background material. Instructors could easily compile concise sub-sections of the book for readings.

The presentation of topics differs somewhat from the standard introductory social science statistics textbooks I have used before. However, the modularity allows the instructor and student to work through the discrete sections in the desired order.

Interface rating: 4

For the most part the display of all images/charts is good and navigation is straightforward. One concern is that the organization of the Table of Contents does not exactly match the organizational outline at the start of each chapter in the PDF version. For example, sometimes there are more detailed sub-headings at the start of chapter and occasionally slightly different section headings/titles. There are also inconsistencies in section listings at start of chapters vs. start of sub-sections.

The text is easy to read and free from any obvious grammatical errors.

Although some of the examples are outdated, I did not review any that were offensive. One example of an outdated reference is using descriptive data on “Men per 100 Women” in U.S. cities as “useful if we are looking for an opposite-sex partner”.

This is a good introduction level statistics text book if you have a course with students who may be intimated by longer texts with more detailed information. Just the core basics are provided here and it is easy to select the sections you need. It is a good text if you plan to supplement with an array of your own materials (lectures, practice, etc.) that are specifically tailored to your discipline (e.g., criminal justice and criminology). Be advised that some formulas use different notation than other standard texts, so you will need to point that out to students if they differ from your lectures or assessment materials.

Reviewed by Shahar Boneh, Professor, Metropolitan State University of Denver on 3/26/21, updated 4/22/21

The textbook is indeed quite comprehensive. It can accommodate any style of introductory statistics course. read more

The textbook is indeed quite comprehensive. It can accommodate any style of introductory statistics course.

The text seems to be statistically accurate.

It is a little too extensive, which requires instructors to cover it selectively, and has a potential to confuse the students.

It is written clearly.

Consistency rating: 4

The terminology is fairly consistent. There is room for some improvement.

By the nature of the subject, the topics have to be presented in a sequential and coherent order. However, the book breaks things down quite effectively.

Organization/Structure/Flow rating: 3

Some of the topics are interleaved and not presented in the order I would like to cover them.

Good interface.

The grammar is ok.

The book seems to be culturally neutral, and not offensive in any way.

I really liked the simulations that go with the book. Parts of the book are a little too advanced for students who are learning statistics for the first time.

Reviewed by Julie Gray, Adjunct Assistant Professor, University of Texas at Arlington on 2/26/21

The textbook is for beginner-level students. The concept development is appropriate--there is always room to grow to high higher level, but for an introduction, the basics are what is needed. This is a well-thought-through OER textbook project by... read more

I found all the material accurate.

Essentially, statistical concepts at the introductory level are accepted as universal. This suggests that the relevance of this textbook will continue for a long time.

The book is well written for introducing beginners to statistical concepts. The figures, tables, and animated examples reinforce the clarity of the written text.

Yes, the information is consistent; when it is introduced in early chapters it ties in well in later chapters that build on and add more understanding for the topic.

Modularity rating: 4

The book is well-written with attention to modularity where possible. Due to the nature of statistics, that is not always possible. The content is presented in the order that I usually teach these concepts.

The organization of the book is good, I particularly like the sample lecture slide presentations and the problem set with solutions for use in quizzes and exams. These are available by writing to the author. It is wonderful to have access to these helpful resources for instructors to use in preparation.

I did not find any interface issues.

The book is well written. In my reading I did not notice grammatical errors.

For this subject and in the examples given, I did not notice any cultural issues.

For the field of social work where qualitative data is as common as quantitative, the importance of giving students the rationale or the motivation to learn the quantitative side is understated. To use this text as an introductory statistics OER textbook in a social work curriculum, the instructor will want to bring in field-relevant examples to engage and motivate students. The field needs data-driven decision making and evidence-based practices to become more ubiquitous than not. Preparing future social workers by teaching introductory statistics is essential to meet that goal.

Reviewed by Mamata Marme, Assistant Professor, Augustana College on 6/25/19

This textbook offers a fairly comprehensive summary of what should be discussed in an introductory course in Statistics. The statistical literacy exercises are particularly interesting. It would be helpful to have the statistical tables... read more

Comprehensiveness rating: 4 see less

The terminology and notation used in the textbook is pretty standard. The content is accurate.

The statistical literacy example are up to date but will need to be updated fairly regularly to keep the textbook fresh. The applications within the chapter are accessible and can be used fairly easily over a couple of editions.

The textbook does not necessarily explain the derivation of some of the formulae and this will need to be augmented by the instructor in class discussion. What is beneficial is that there are multiple ways that a topic is discussed using graphs, calculations and explanations of the results. Statistics textbooks have to cover a wide variety of topics with a fair amount of depth. To do this concisely is difficult. There is a fine line between being concise and clear, which this textbook does well, and being somewhat dry. It may be up to the instructor to bring case studies into the readings we are going through the topics rather than wait until the end of the chapter.

The textbook uses standard notation and terminology. The heading section of each chapter is closely tied to topics that are covered. The end of chapter problems and the statistical literacy applications are closely tied to the material covered.

The authors have done a good job treating each chapter as if they stand alone. The lack of connection to a past reference may create a sense of disconnect between the topics discussed

The text's "modularity" does make the flow of the material a little disconnected. If would be better if there was accountability of what a student should already have learnt in a different section. The earlier material is easy to find but not consistently referred to in the text.

I had no problem with the interface. The online version is more visually interesting than the pdf version.

I did not see any grammatical errors.

Cultural Relevance rating: 4

I am not sure how to evaluate this. The examples are mostly based on the American experience and the data alluded to mostly domestic. However, I am not sure if that creates a problem in understanding the methodology.

Overall, this textbook will cover most of the topics in a survey of statistics course.

Reviewed by Alexandra Verkhovtseva, Professor, Anoka-Ramsey Community College on 6/3/19

This is a comprehensive enough text, considering that it is not easy to create a comprehensive statistics textbook. It is suitable for an introductory statistics course for non-math majors. It contains twenty-one chapters, covering the wide range... read more

The content is pretty accurate, I did not find any biases or errors.

The book contains fairly recent data presented in the form of exercises, examples and applications. The topics are up-to-date, and appropriate technology is used for examples, applications, and case studies.

The language is simple and clear, which is a good thing, since students are usually scared of this class, and instructors are looking for something to put them at ease. I would, however, try to make it a little more interesting, exciting, or may be even funny.

Consistency is good, the book has a great structure. I like how each chapter has prerequisites and learner outcomes, this gives students a good idea of what to expect. Material in this book is covered in good detail.

The text can be easily divided into sub-sections, some of which can be omitted if needed. The chapter on regression is covered towards the end (chapter 14), but part of it can be covered sooner in the course.

The book contains well organized chapters that makes reading through easy and understandable. The order of chapters and sections is clear and logical.

The online version has many functions and is easy to navigate. This book also comes with a PDF version. There is no distortion of images or charts. The text is clean and clear, the examples provided contain appropriate format of data presentation.

No grammatical errors found.

The text uses simple and clear language, which is helpful for non-native speakers. I would include more culturally-relevant examples and case studies. Overall, good text.

In all, this book is a good learning experience. It contains tools and techniques that free and easy to use and also easy to modify for both, students and instructors. I very much appreciate this opportunity to use this textbook at no cost for our students.

Reviewed by Dabrina Dutcher, Assistant Professor, Bucknell University on 3/4/19

This is a reasonably thorough first-semester statistics book for most classes. It would have worked well for the general statistics courses I have taught in the past but is not as suitable for specialized introductory statistics courses for engineers or business applications. That is OK, they have separate texts for that! The only sections that feel somewhat light in terms of content are the confidence intervals and ANOVA sections. Given that these topics are often sort of crammed in at the end of many introductory classes, that might not be problematic for many instructors. It should also be pointed out that while there are a couple of chapters on probability, this book spends presents most formulas as "black boxes" rather than worry about the derivation or origin of the formulas. The probability sections do not include any significant combinatorics work, which is sometimes included at this level.

I did not find any errors in the formulas presented but I did not work many end-of-chapter problems to gauge the accuracy of their answers.

There isn't much changing in the introductory stats world, so I have no concerns about the book becoming outdated rapidly. The examples and problems still feel relevant and reasonably modern. My only concern is that the statistical tool most often referenced in the book are TI-83/84 type calculators. As students increasingly buy TI-89s or Inspires, these sections of the book may lose relevance faster than other parts.

Solid. The book gives a list of key terms and their definitions at the end of each chapter which is a nice feature. It also has a formula review at the end of each chapter. I can imagine that these are heavily used by students when studying! Formulas are easy to find and read and are well defined. There are a few areas that I might have found frustrating as a student. For example, the explanation for the difference in formulas for a population vs sample standard deviation is quite weak. Again, this is a book that focuses on sort of a "black-box" approach but you may have to supplement such sections for some students.

I did not detect any problems with inconsistent symbol use or switches in terminology.

Modularity rating: 3

This low rating should not be taken as an indicator of an issue with this book but would be true of virtually any statistics book. Different books still use different variable symbols even for basic calculated statistics. So trying to use a chapter of this book without some sort of symbol/variable cheat-sheet would likely be frustrating to the students.

However, I think it would be possible to skip some chapters or use the chapters in a different order without any loss of functionality.

This book uses a very standard order for the material. The chapter on regressions comes later than it does in some texts but it doesn't really matter since that chapter never seems to fit smoothly anywhere.

There are numerous end of chapter problems, some with answers, available in this book. I'm vacillating on whether these problems would be more useful if they were distributed after each relevant section or are better clumped at the end of the whole chapter. That might be a matter of individual preference.

I did not detect any problems.

I found no errors. However, there were several sections where the punctuation seemed non-ideal. This did not affect the over-all useability of the book though

I'm not sure how well this book would work internationally as many of the examples contain domestic (American) references. However, I did not see anything offensive or biased in the book.

Reviewed by Ilgin Sager, Assistant Professor, University of Missouri - St. Louis on 1/14/19

As the title implies, this is a brief introduction textbook. It covers the fundamental of the introductory statistics, however not a comprehensive text on the subject. A teacher can use this book as the sole text of an introductory statistics. The prose format of definitions and theorems make theoretical concepts accessible to non-math major students. The textbook covers all chapters required in this level course.

It is accurate; the subject matter in the examples to be up to date, is timeless and wouldn't need to be revised in future editions; there is no error except a few typographical errors. There are no logic errors or incorrect explanations.

This text will remain up to date for a long time since it has timeless examples and exercises, it wouldn't be outdated. The information is presented clearly with a simple way and the exercises are beneficial to follow the information.

The material is presented in a clear, concise manner. The text is easy readable for the first time statistics student.

The structure of the text is very consistent. Topics are presented with examples, followed by exercises. Problem sets are appropriate for the level of learner.

When the earlier matters need to be referenced, it is easy to find; no trouble reading the book and finding results, it has a consistent scheme. This book is set very well in sections.

The text presents the information in a logical order.

The learner can easily follow up the material; there is no interface problem.

There is no logic errors and incorrect explanations, a few typographical errors is just to be ignored.

Not applicable for this textbook.

Reviewed by Suhwon Lee, Associate Teaching Professor, University of Missouri on 6/19/18

This book is pretty comprehensive for being a brief introductory book. This book covers all necessary content areas for an introduction to Statistics course for non-math majors. The text book provides an effective index, plenty of exercises, review questions, and practice tests. It provides references and case studies. The glossary and index section is very helpful for students and can be used as a great resource.

Content appears to be accurate throughout. Being an introductory book, the book is unbiased and straight to the point. The terminology is standard.

The content in textbook is up to date. It will be very easy to update it or make changes at any point in time because of the well-structured contents in the textbook.

The author does a great job of explaining nearly every new term or concept. The book is easy to follow, clear and concise. The graphics are good to follow. The language in the book is easily understandable. I found most instructions in the book to be very detailed and clear for students to follow.

Overall consistency is good. It is consistent in terms of terminology and framework. The writing is straightforward and standardized throughout the text and it makes reading easier.

The authors do a great job of partitioning the text and labeling sections with appropriate headings. The table of contents is well organized and easily divisible into reading sections and it can be assigned at different points within the course.

Organization/Structure/Flow rating: 4

Overall, the topics are arranged in an order that follows natural progression in a statistics course with some exception. They are addressed logically and given adequate coverage.

The text is free of any issues. There are no navigation problems nor any display issues.

The text contains no grammatical errors.

The text is not culturally insensitive or offensive in any way most of time. Some examples might need to consider citing the sources or use differently to reflect current inclusive teaching strategies.

Overall, it's well-written and good recourse to be an introduction to statistical methods. Some materials may not need to be covered in an one-semester course. Various examples and quizzes can be a great recourse for instructor.

Reviewed by Jenna Kowalski, Mathematics Instructor, Anoka-Ramsey Community College on 3/27/18

The text includes the introductory statistics topics covered in a college-level semester course. An effective index and glossary are included, with functional hyperlinks. read more

The text includes the introductory statistics topics covered in a college-level semester course. An effective index and glossary are included, with functional hyperlinks.

Content Accuracy rating: 3

The content of this text is accurate and error-free, based on a random sampling of various pages throughout the text. Several examples included information without formal citation, leading the reader to potential bias and discrimination. These examples should be corrected to reflect current values of inclusive teaching.

The text contains relevant information that is current and will not become outdated in the near future. The statistical formulas and calculations have been used for centuries. The examples are direct applications of the formulas and accurately assess the conceptual knowledge of the reader.

The text is very clear and direct with the language used. The jargon does require a basic mathematical and/or statistical foundation to interpret, but this foundational requirement should be met with course prerequisites and placement testing. Graphs, tables, and visual displays are clearly labeled.

The terminology and framework of the text is consistent. The hyperlinks are working effectively, and the glossary is valuable. Each chapter contains modules that begin with prerequisite information and upcoming learning objectives for mastery.

The modules are clearly defined and can be used in conjunction with other modules, or individually to exemplify a choice topic. With the prerequisite information stated, the reader understands what prior mathematical understanding is required to successfully use the module.

The topics are presented well, but I recommend placing Sampling Distributions, Advanced Graphs, and Research Design ahead of Probability in the text. I think this rearranged version of the index would better align with current Introductory Statistics texts. The structure is very organized with the prerequisite information stated and upcoming learner outcomes highlighted. Each module is well-defined.

Adding an option of returning to the previous page would be of great value to the reader. While progressing through the text systematically, this is not an issue, but when the reader chooses to skip modules and read select pages then returning to the previous state of information is not easily accessible.

No grammatical errors were found while reviewing select pages of this text at random.

Cultural Relevance rating: 3

Several examples contained data that were not formally cited. These examples need to be corrected to reflect current inclusive teaching strategies. For example, one question stated that “while men are XX times more likely to commit murder than women, …” This data should be cited, otherwise the information can be interpreted as biased and offensive.

An included solutions manual for the exercises would be valuable to educators who choose to use this text.

Reviewed by Zaki Kuruppalil, Associate Professor, Ohio University on 2/1/18

This is a comprehensive book on statistical methods, its settings and most importantly the interpretation of the results. With the advent of computers and software’s, complex statistical analysis can be done very easily. But the challenge is the knowledge of how to set the case, setting parameters (for example confidence intervals) and knowing its implication on the interpretation of the results. If not done properly this could lead to deceptive inferences, inadvertently or purposely. This book does a great job in explaining the above using many examples and real world case studies. If you are looking for a book to learn and apply statistical methods, this is a great one. I think the author could consider revising the title of the book to reflect the above, as it is more than just an introduction to statistics, may be include the word such as practical guide.

The contents of the book seems accurate. Some plots and calculations were randomly selected and checked for accuracy.

The book topics are up to date and in my opinion, will not be obsolete in the near future. I think the smartest thing the author has done is, not tied the book with any particular software such as minitab or spss . No matter what the software is, standard deviation is calculated the same way as it is always. The only noticeable exception in this case was using the Java Applet for calculating Z values in page 261 and in page 416 an excerpt of SPSS analysis is provided for ANOVA calculations.

The contents and examples cited are clear and explained in simple language. Data analysis and presentation of the results including mathematical calculations, graphical explanation using charts, tables, figures etc are presented with clarity.

Terminology is consistant. Framework for each chapter seems consistent with each chapter beginning with a set of defined topics, and each of the topic divided into modules with each module having a set of learning objectives and prerequisite chapters.

The text book is divided into chapters with each chapter further divided into modules. Each of the modules have detailed learning objectives and prerequisite required. So you can extract a portion of the book and use it as a standalone to teach certain topics or as a learning guide to apply a relevant topic.

Presentation of the topics are well thought and are presented in a logical fashion as if it would be introduced to someone who is learning the contents. However, there are some issues with table of contents and page numbers, for example chapter 17 starts in page 597 not 598. Also some tables and figures does not have a number, for instance the graph shown in page 114 does not have a number. Also it would have been better if the chapter number was included in table and figure identification, for example Figure 4-5 . Also in some cases, for instance page 109, the figures and titles are in two different pages.

No major issues. Only suggestion would be, since each chapter has several modules, any means such as a header to trace back where you are currently, would certainly help.

Grammatical Errors rating: 4

Easy to read and phrased correctly in most cases. Minor grammatical errors such as missing prepositions etc. In some cases the author seems to have the habbit of using a period after the decimal. For instance page 464, 467 etc. For X = 1, Y' = (0.425)(1) + 0.785 = 1.21. For X = 2, Y' = (0.425)(2) + 0.785 = 1.64.

However it contains some statements (even though given as examples) that could be perceived as subjective, which the author could consider citing the sources. For example from page 11: Statistics include numerical facts and figures. For instance: • The largest earthquake measured 9.2 on the Richter scale. • Men are at least 10 times more likely than women to commit murder. • One in every 8 South Africans is HIV positive. • By the year 2020, there will be 15 people aged 65 and over for every new baby born.

Solutions for the exercises would be a great teaching resource to have

Reviewed by Randy Vander Wal, Professor, The Pennsylvania State University on 2/1/18

As a text for an introductory course, standard topics are covered. It was nice to see some topics such as power, sampling, research design and distribution free methods covered, as these are often omitted in abbreviated texts. Each module introduces the topic, has appropriate graphics, illustration or worked example(s) as appropriate and concluding with many exercises. An instructor’s manual is available by contacting the author. A comprehensive glossary provides definitions for all the major terms and concepts. The case studies give examples of practical applications of statistical analyses. Many of the case studies contain the actual raw data. To note is that the on-line e-book provides several calculators for the essential distributions and tests. These are provided in lieu of printed tables which are not included in the pdf. (Such tables are readily available on the web.)

The content is accurate and error free. Notation is standard and terminology is used accurately, as are the videos and verbal explanations therein. Online links work properly as do all the calculators. The text appears neutral and unbiased in subject and content.

The text achieves contemporary relevance by ending each section with a Statistical Literacy example, drawn from contemporary headlines and issues. Of course, the core topics are time proven. There is no obvious material that may become “dated”.

The text is very readable. While the pdf text may appear “sparse” by absence varied colored and inset boxes, pictures etc., the essential illustrations and descriptions are provided. Meanwhile for this same content the on-line version appears streamlined, uncluttered, enhancing the value of the active links. Moreover, the videos provide nice short segments of “active” instruction that are clear and concise. Despite being a mathematical text, the text is not overly burdened by formulas and numbers but rather has “readable feel”.

This terminology and symbol use are consistent throughout the text and with common use in the field. The pdf text and online version are also consistent by content, but with the online e-book offering much greater functionality.

The chapters and topics may be used in a selective manner. Certain chapters have no pre-requisite chapter and in all cases, those required are listed at the beginning of each module. It would be straightforward to select portions of the text and reorganize as needed. The online version is highly modular offering students both ease of navigation and selection of topics.

Chapter topics are arranged appropriately. In an introductory statistics course, there is a logical flow given the buildup to the normal distribution, concept of sampling distributions, confidence intervals, hypothesis testing, regression and additional parametric and non-parametric tests. The normal distribution is central to an introductory course. Necessary precursor topics are covered in this text, while its use in significance and hypothesis testing follow, and thereafter more advanced topics, including multi-factor ANOVA.

Each chapter is structured with several modules, each beginning with pre-requisite chapter(s), learning objectives and concluding with Statistical Literacy sections providing a self-check question addressing the core concept, along with answer, followed by an extensive problem set. The clear and concise learning objectives will be of benefit to students and the course instructor. No solutions or answer key is provided to students. An instructor’s manual is available by request.

The on-line interface works well. In fact, I was pleasantly surprised by its options and functionality. The pdf appears somewhat sparse by comparison to publisher texts, lacking pictures, colored boxes, etc. But the on-line version has many active links providing definitions and graphic illustrations for key terms and topics. This can really facilitate learning as making such “refreshers” integral to the new material. Most sections also have short videos that are professionally done, with narration and smooth graphics. In this way, the text is interactive and flexible, offering varied tools for students. To note is that the interactive e-book works for both IOS and OS X.

The text in pdf form appeared to free of grammatical errors, as did the on-line version, text, graphics and videos.

This text contains no culturally insensitive or offensive content. The focus of the text is on concepts and explanation.

The text would be a great resource for students. The full content would be ambitious for a 1-semester course, such use would be unlikely. The text is clearly geared towards students with no statistics background nor calculus. The text could be used in two styles of course. For 1st year students early chapters on graphs and distributions would be the starting point, omitting later chapters on Chi-square, transformations, distribution-free and size effect chapters. Alternatively, for upper level students the introductory chapters could be bypassed with the latter chapters then covered to completion.

This text adopts a descriptive style of presentation with topics well and fully explained, much like the “Dummy series”. For this, it may seem a bit “wordy”, but this can well serve students and notably it complements powerpoint slides that are generally sparse on written content. This text could be used as the primary text, for regular lectures, or as reference for a “flipped” class. The e-book videos are an enabling tool if this approach is adopted.

Reviewed by David jabon, Associate Professor, DePaul University on 8/15/17

This text covers all the standard topics in a semester long introductory course in statistics. It is particularly well indexed and very easy to navigate. There is comprehensive hyperlinked glossary. read more

This text covers all the standard topics in a semester long introductory course in statistics. It is particularly well indexed and very easy to navigate. There is comprehensive hyperlinked glossary.

The material is completely accurate. There are no errors. The terminology is standard with one exception: the book calls what most people call the interquartile range, the H-spread in a number of places. Ideally, the term "interquartile range" would be used in place of every reference to "H-spread." "Interquartile range" is simply a better, more descriptive term of the concept that it describes. It is also more commonly used nowadays.

This book came out a number of years ago, but the material is still up to date. Some more recent case studies have been added.

The writing is very clear. There are also videos for almost every section. The section on boxplots uses a lot of technical terms that I don't find are very helpful for my students (hinge, H-spread, upper adjacent value).

The text is internally consistent with one exception that I noted (the use of the synonymous words "H-spread" and "interquartile range").

The text book is brokenly into very short sections, almost to a fault. Each section is at most two pages long. However at the end of each of these sections there are a few multiple choice questions to test yourself. These questions are a very appealing feature of the text.

The organization, in particular the ordering of the topics, is rather standard with a few exceptions. Boxplots are introduced in Chapter II before the discussion of measures of center and dispersion. Most books introduce them as part of discussion of summaries of data using measure of center and dispersion. Some statistics instructors may not like the way the text lumps all of the sampling distributions in a single chapter (sampling distribution of mean, sampling distribution for the difference of means, sampling distribution of a proportion, sampling distribution of r). I have tried this approach, and I now like this approach. But it is a very challenging chapter for students.

The book's interface has no features that distracted me. Overall the text is very clean and spare, with no additional distracting visual elements.

The book contains no grammatical errors.

The book's cultural relevance comes out in the case studies. As of this writing there are 33 such case studies, and they cover a wide range of issues from health to racial, ethnic, and gender disparity.

Each chapter as a nice set of exercises with selected answers. The thirty three case studies are excellent and can be supplement with some other online case studies. An instructor's manual and PowerPoint slides can be obtained by emailing the author. There are direct links to online simulations within the text. This text is very high quality textbook in every way.

1. Introduction
2. Graphing Distributions
3. Summarizing Distributions
4. Describing Bivariate Data
5. Probability
6. Research Design
7. Normal Distributions
8. Advanced Graphs
9. Sampling Distributions
10. Estimation
11. Logic of Hypothesis Testing
12. Testing Means
14. Regression
15. Analysis of Variance
16. Transformations
17. Chi Square
18. Distribution-Free Tests
19. Effect Size
20. Case Studies
21. Glossary

Ancillary Material

Ancillary materials are available by contacting the author or publisher .

About the Book

Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.

About the Contributors

David Lane is an Associate Professor in the Departments of Psychology, Statistics, and Management at the Rice University. Lane is the principal developer of this resource although many others have made substantial contributions. This site was developed at Rice University, University of Houston-Clear Lake, and Tufts University.

Contribute to this Page

What is Statistics? Importance, Scope, Limitations

Post last modified: 30 July 2022
Reading time: 24 mins read
Post category: Business Statistics

What is Statistics?

Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.

Statistics is a set of decision-making techniques which helps businessmen in making suitable policies from the available data. In fact, every businessman needs a sound background of statistics as well as of mathematics.

The purpose of statistics and mathematics is to manipulate, summarize and investigate data so that the useful decision-making results can be executed.

Table of Content

1 What is Statistics?
2 Statistics Meaning
3 Statistics Definition
4.1 Uses of Statistics in Business
4.2 Uses of Mathematics for Decision Making
4.3 Uses of Statistics in Economics
5.1 Condensation
5.2 Comparison
5.3 Forecast
5.4 Testing of hypotheses
5.5 Preciseness
5.6 Expectation
6.1 Importance of Statistics in Business and Industry
6.2 Importance in the Field of Science and Research
6.3 Importance in the Field of Banking
6.4 Importance to the State
6.5 Importance in planning
7.1 Presents facts in numerical figures
7.2 Presents complex facts in a simplified form
7.3 Studies relationship between two or more phenomena
7.4 Helps in the formulation of policies
7.5 Helps in forecasting
7.6 Provides techniques for testing of hypothesis
7.7 Provides techniques for making decisions under uncertainty
8.1 Statistics Suits to the Study of Quantitative Data Only
8.2 Statistical Results are not Exact
8.3 Statistics Deals with Aggregates Only
8.4 Statistics is Useful for Experts Only
8.5 Statistics does not Provide Solutions to the Problems

Statistics Meaning

The term ‘statistics’ has been derived from the Latin word ‘status’ Italian word ‘statista’ or German word ‘statistik’.

All these words mean ‘Political state’. In ancient days, the states were required to collect statistical data mainly for the number of youngmen so that they can be recruited in the Army.

Also to calculate the total amount of land revenue that can be collected. Due to this reason, statistics is also called ‘Political Arithmetic’.

Statistics Definition

Statistics has been defined in different ways by different authors.

Uses of Statistics in Business Decision Making

Uses of statistics in business.

The following are the main uses of statistics in various business activities:

With the help of statistical methods, quantitative information about production, sale, purchase, finance, etc. can be obtained. This type of information helps businessmen in formulating suitable policies.
By using the techniques of time series analysis which are based on statistical methods, the businessman can predict the effect of a large number of variables with a fair degree of accuracy.
In business decision theory, most of the statistics techniques are used in taking a business decision which helps us in doing the business without uncertainty.
Nowadays, a large part of modern business is being organised around systems of statistical analysis and control.
By using ‘Bayesian Decision Theory’, the businessmen can select the optimal decisions for the direct evaluation of the payoff for each alternative course of action.

Uses of Mathematics for Decision Making

The number of defects in a roll of paper, bale of cloth, sheet of a photographic film can be judged by means of Control Chart based on Normal distribution.
In statistical quality control, we analyse the data which are based on the principles involved in Normal curve.

Uses of Statistics in Economics

Statistics is the basis of economics. The consumer’s maximum satisfaction can be determined on the basis of data pertaining to income and expenditure. The various laws of demand depend on the data concerning price and quantity. The price of a commodity is well determined on the basis of data relating to its buyers, sellers, etc.

Functions of Statistics

Statistics can be well-defined as a branch of research which is concerned with the development and application of techniques for collecting, organising, presenting, analysing and interpreting data in such a manner that the reliability of conclusions may be evaluated in terms of probability statements.

Statistical methods and processes are useful for business development and, hence, applied to enormous numerical facts with an objective that “behind every figure, there’s a story”.

Some key functions of statistics are as follows:

Condensation

Testing of hypotheses, preciseness, expectation.

Statistics can be used to compress a large amount of data into small meaningful information; for example, aggregated sales forecast, BSE indices, GDP growth rate, etc. It is almost impossible to get a complete idea of the profitability of a company by looking at the records of its income and expenditure. Financial ratios such as return on investment, earnings per share, profit margins, etc., however, can be easily remembered and thus can be used in quick decision making.

Statistics facilitate comparing different quantities. For example, the price-to-earnings ratio of ITC as of January 22, 2021 is 19.54 as compared to HUL. HUL is overvalued, quoting a price-to-earnings ratio of 71 times.

Statistics helps forecast by looking at trends of a variable. It is essential for planning and decision-making. Predictions or forecasts based on intuition can be disastrous for any business.

For example, to decide the production capacity for a vehicle-manufacturing plant, we need to predict the demand for the product mix, supply of components, cost of manpower, competitor strategy, etc., over the next 5 to 10 years, before committing an investment.

Hypotheses are statements about population parameters based on knowledge from literature that a researcher would like to test for validity in the light of new information. Drawing inferences about the population using sample estimates involves an element of risk.

Statistics visualises and presents facts precisely in a quantitative form. Facts and information conveyed in quantitative terms are more convincing than qualitative data. For example, ‘increase in profit margin is less in the year 2020 than in the year 2019’ does not convey a precise and complete piece of information.

On the other hand, statistics summarise the information more precisely. For example, ‘profit margin is 5% of the turnover in the year 2020 against 7% in the year 2019’.

Statistics can act as the basic building block for framing clear plans and policies. For example, how much raw material to be imported in a year, how much capacity to be expanded, or manpower to be recruited, etc., depends on the expected value of outcome of our decisions taken under different situations.

Importance of Statistics

Statistics in today’s life has become an essential part of various business activities which is clear from the following points.

The importance of statistics in the following major areas:

Importance of Statistics in Business and Industry

Importance in the field of science and research, importance in the field of banking, importance to the state, importance in planning.

In past days, decisions regarding business were made only on personal judgement. However, in these days, they are based on several mathematical and statistical techniques and the best decision is arrived by using all these techniques.

For example, by using the testing hypothesis, we can reject or accept the null hypothesis which are based upon the assumption made from the population or universe

By using ‘Bayesian Decision Theory’ or ‘Decision Theory’, we can select the optimal decisions for the direct evaluation of the payoff for each alternative course of action.

Mathematics and statistics have become ingredients of various decisions problems which is clear from the following:

In Selecting Alternative Course of Action: The process of business decisions involve the selection of a single action among some set of alternative actions. When there are two or more alternative courses of action, and we need only one course of action, statistical decisions theory helps us in selecting the required course of action by applying Bayesian decision theory and thus saves lot of time.
In Removing Uncertainty: In decision-making problems, uncertainty is very common in a situation, when the course of action is not known to us. When there are many possible outcomes of an event, we cannot predict with certainty that what will happen. By applying the concept of joint and conditional probability, the uncertainty about the event can be removed very easily.
In Calculating E.O.L., C.O.L., etc.: In business, the opportunity loss is very often, which can be defined as the difference between the highest possible profit for an event and the actual profit obtained for the actual action taken. The expected opportunity loss (E.O.L.) and conditional opportunity loss (C.O.L.) can be easily calculated by using the concept of maximum and minimum criteria of pay-off.

Statistics has great significance in the field of physical and natural sciences. It is widely used in verifying scientific laws and phenomenon.

For example, to formulate standards of body temperature, pulse rate, blood pressure, etc. The success of modern computers depends on the conclusions drawn on the basis of statistics.

In banking industry, the bankers have to relate demand deposits, time deposits, credit etc. It is on the basis of data relating to demand and time deposits that the bankers determine the credit policies. The credit policies are based on the theory of probability.

We know that the subject of statistics originated for helping the ancient rulers in the assessment of their military and economic strength. Gradually its scope was enlarged to tackle other problems relating to political activities of the State.

In the modern era, the role of State has increased and various governments of the world also take care of the welfare of its people. Therefore, these governments require much greater information in the form of numerical figures for the fulfilment of welfare objectives in addition to the efficient running of their administration.

Planning is indispensable for achieving faster rate of growth through the best use of a nation’s resources. It also requires a good deal of statistical data on various aspects of the economy.

One of the aims of planning could be to achieve a specified rate of growth of the economy. Using statistical techniques, it is possible to assess the amounts of various resources available in the economy and accordingly determine whether the specified rate of growth is sustainable or not.

Scope of Statistics

The following are the main scope of statistics:

Presents facts in numerical figures

Presents complex facts in a simplified form, studies relationship between two or more phenomena, helps in the formulation of policies, helps in forecasting, provides techniques for testing of hypothesis, provides techniques for making decisions under uncertainty.

The first function of statistics is to present a given problem in terms of numerical figures. We know that the numerical presentation helps in having a better understanding of nature an of problem.

Generally, a problem to be investigated is represented by a large mass of numerical figures which are very difficult to understand and remember. Using various statistical methods, this large mass of data can be presented in a simplified form.

Statistics can be used to investigate whether two or more phenomena are related. For example, the relationship between income and consumption, demand and supply, etc.

Statistical analysis of data is the starting point in the formulation of policies in various economic, business and government activities. For example, using statistical techniques a firm can know the tastes and preferences of the consumers and decide to make its product accordingly.

The success of planning by the Government or of a business depends to a large extent upon the accuracy of their forecasts. Statistics provides a scientific basis for making such forecasts.

A hypothesis is a statement about some characteristics of a population (or universe).

Many times we face an uncertain situation where any one of the many alternatives may be adopted. A businessman might face a situation of uncertain investment opportunities in which he can lose or gain.

He may be interested in knowing whether to undertake a particular investment or not. The answer to such problems are provided by the statistical techniques of decision-making under uncertainty.

Limitations of Statistics

Statistics is considered to be a science as well as an art, which is used as an instrument of research in almost every sphere of our activities.

Some of the limitations of statistics are as follows:

Statistics Suits to the Study of Quantitative Data Only

Statistical results are not exact, statistics deals with aggregates only, statistics is useful for experts only, statistics does not provide solutions to the problems.

Statistics deals with the study of quantitative data only. By using the methods of statistics, the problems regarding production, income, price, wage, height, weight etc. can be studied. Such characteristics are quantitative in nature.

The characteristics like honesty, goodwill, duty, character, beauty, intelligence, efficiency, integrity etc. are not capable of quantitative measurement and hence cannot be directly dealt with statistical methods. These characteristics are qualitative in nature.

In such type of characteristics, only comparison is possible The use of statistical methods is limited to quantitative characteristics and those qualitative characteristics which are capable of being expressed numerically.

The task of statistical analysis is performed under certain conditions. It is not always possible, rather not advisable, to consider the entire population during statistical investigations.

The use of samples is called for in statistical investigations. And the results obtained by using samples may not be universally true for the entire population. Data collected for a statistical enquiry may not be hundred percent true. Statistical results are true on an average.

Statistics does not recognise individual items. Consider the statement, “The weight of Mr X in the college is 70 kg”. This statement does not constitute statistical data. Statistical methods are not going to investigate anything about this statement. Whereas, if the weights of all the students of the college are given, the statistical methods may be applied to analyse that data.

According to Tippett, “Statistics is essentially totalitarian because it is not concerned with individual values, but only with classes”. Statistics is used to study group characteristics of aggregates.

Statistics is both a science and an art. It is systematic and finds applications in studying problems in Economics, Business, Astronomy, Physics, Medicines etc. Statistical methods are sophisticated in nature. Everyone is not expected to possess the intelligence required to understand and to apply these methods to practical problems. This is the job of an expert, who is well-versed with statistical methods

The statistical methods are used to explore the essentials of problems. It does not find use in inventing solutions to problems. For example, the methods of statistics may reveal the fact that the average result of a particular class in a college is deteriorating for the last ten years, i.e., the trend of the result is downward, but statistics cannot provide solution to this problem.

It cannot help in taking remedial steps to improve the result of that class. Statistics should be taken as a means and not as an end. The methods of statistics are used to study the various aspects of the data.

Statistics is a set of decision-making techniques which helps businessmen in making suitable policies from the available data.
“Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.”
With the help of statistical methods, quantitative information about production, sale, purchase, finance etc. can be obtained.
Statistics is the basis of economics. The consumer’s maximum satisfaction can be determined on the basis of data pertaining to income and expenditure.
W.I. King says, “Statistics is a most useful servant but only of great value to those who understand its proper use.”
Yule and Kendall has rightly said that “statistical methods are most dangerous tools in the hands of inexperts.”
The statistical methods are used to explore the essentials of problems.

What is consumer research developing, collecting, designing, this post has 8 comments.

It was really helpful, the info was quite well. though if it would be good if you increase the amount of info’s to get a deep view

Thanks for your valuable feedback. Our team will connect with you in a bit.

Compact and sleek !! Great

Thank you so much It’s realy helpful information availble

Thanks you too, and please am a first year student, I would like you to update more with the knowledge of statistic.

Thank u so much. This information is very helpful. I am very lucky to seen this information.

I really appreciate this service for it has been helpful to me.

very useful

World's Best Online Courses at One Place

We’ve spent the time in finding, so you can spend your time in learning

Digital Marketing

Personal Growth

Development

Search Search Please fill out this field.

What Is Statistics?

Understanding statistics.

Descriptive & Inferential Statistics

Mean, Median, and Mode

Understanding statistical data.

Levels of Measurement
Sampling Techniques

Uses of Statistics

The bottom line.

Corporate Finance
Financial Analysis

Statistics: Definition, Types, and Importance

Katrina Ávila Munichiello is an experienced editor, writer, fact-checker, and proofreader with more than fourteen years of experience working with print and online publications.

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory.

People who do statistics are referred to as statisticians. They’re particularly concerned with determining how to draw reliable conclusions about large groups and general events from the behavior and other observable characteristics of small samples. These small samples represent a portion of the large group or a limited number of instances of a general phenomenon.

Key Takeaways

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
The two major areas of statistics are descriptive and inferential statistics.
Statistics can be communicated at different levels ranging from non-numerical descriptor (nominal-level) to numerical in reference to a zero-point (ratio-level).
Several sampling techniques can be used to compile statistical data, including simple random, systematic, stratified, or cluster sampling.
Statistics are present in almost every department of every company and are an integral part of investing.

Dennis Madamba / Investopedia

Statistics are used in virtually all scientific disciplines, such as the physical and social sciences as well as in business, medicine, the humanities, government, and manufacturing. Statistics is fundamentally a branch of applied mathematics that developed from the application of mathematical tools, including calculus and linear algebra, to probability theory.

In practice, statistics is the idea that we can learn about the properties of large sets of objects or events (a population ) by studying the characteristics of a smaller number of similar objects or events (a sample ). Gathering comprehensive data about an entire population is too costly, difficult, or impossible in many cases, so statistics start with a sample that can be conveniently or affordably observed.

Statisticians measure and gather data about the individuals or elements of a sample and analyze this data to generate descriptive statistics. They can then use these observed characteristics of the sample data, which are properly called “statistics,” to make inferences or educated guesses about the unmeasured characteristics of the broader population, known as the parameters.

Statistics informally dates back centuries. An early record of correspondence between French mathematicians Pierre de Fermat and Blaise Pascal in 1654 is often cited as an early example of statistical probability analysis.

Descriptive and Inferential Statistics

The two major areas of statistics are known as descriptive statistics , which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions. Descriptive statistics include mean (average), variance, skewness , and kurtosis . Inferential statistics include linear regression analysis, analysis of variance (ANOVA), logit/Probit models, and null hypothesis testing.

Descriptive Statistics

Descriptive statistics mostly focus on the central tendency, variability, and distribution of sample data. Central tendency means the estimate of the characteristics, a typical element of a sample or population. It includes descriptive statistics such as mean , median , and mode .

Variability refers to a set of statistics that show how much difference there is among the elements of a sample or population along the characteristics measured. It includes metrics such as range, variance , and standard deviation .

The distribution refers to the overall “shape” of the data, which can be depicted on a chart such as a histogram or a dot plot, and includes properties such as the probability distribution function, skewness, and kurtosis. Descriptive statistics can also describe differences between observed characteristics of the elements of a data set. They can help us understand the collective properties of the elements of a data sample and form the basis for testing hypotheses and making predictions using inferential statistics.

Inferential Statistics

Inferential statistics is a tool that statisticians use to draw conclusions about the characteristics of a population, drawn from the characteristics of a sample. It is also used to determine how certain they can be of the reliability of those conclusions. Based on the sample size and distribution, statisticians can calculate the probability that statistics, which measure the central tendency, variability, distribution, and relationships between characteristics within a data sample, provide an accurate picture of the corresponding parameters of the whole population from which the sample is drawn.

Inferential statistics are used to make generalizations about large groups, such as estimating average demand for a product by surveying the buying habits of a sample of consumers or attempting to predict future events. This might mean projecting the future return of a security or asset class based on returns in a sample period.

Regression analysis is a widely used technique of statistical inference. It is used to determine the strength and nature of the relationship (the correlation) between a dependent variable and one or more explanatory (independent) variables. The output of a regression model is often analyzed for statistical significance, meaning that a result from findings generated by testing or experimentation is not likely to have occurred randomly or by chance. In other words, statistical significance suggests the results are attributable to a specific cause elucidated by the data.

Having statistical significance is important for academic disciplines or practitioners that rely heavily on analyzing data and research.

The terms “mean,” “median,” and “mode” fall under the umbrella of central tendency. They describe an element that’s typical in a given sample group. You can find the mean descriptor by adding the numbers in the group and dividing the result by the number of data set observations.

The middle number in the set is the median. Half of all included numbers are higher than the median, and half are lower. The median home value in a neighborhood would be $350,000 if five homes were located there and valued at $500,000, $400,000, $350,000, $325,000, and $300,000. Two values are higher, and two are lower.

Mode identifies the number that falls between the highest and lowest values. It appears most frequently in the data set.

The root of statistics is driven by variables. A variable is a data set that can be counted that marks a characteristic or attribute of an item. For example, a car can have variables such as make, model, year, mileage, color, or condition. By combining the variables across a set of data, such as the colors of all cars in a given parking lot, statistics allows us to better understand trends and outcomes.

There are two main types of variables:

First, qualitative variables are specific attributes that are often non-numeric. Many of the examples given in the car example are qualitative. Other examples of qualitative variables in statistics are gender, eye color, or city of birth. Qualitative data is most often used to determine what percentage of an outcome occurs for any given qualitative variable. Qualitative analysis often does not rely on numbers. For example, trying to determine what percentage of women own a business analyzes qualitative data.

The second type of variable in statistics is quantitative variables. Quantitative variables are studied numerically and only have weight when they’re about a non-numerical descriptor. Similar to quantitative analysis, this information is rooted in numbers. In the car example above, the mileage driven is a quantitative variable, but the number 60,000 holds no value unless it is understood that it is the total number of miles driven.

Quantitative variables can be further broken into two categories. First, discrete variables have limitations in statistics and infer that there are gaps between potential discrete variable values. The number of points scored in a football game is a discrete variable because:

There can be no decimals.
It is impossible for a team to score only one point.

Statistics also makes use of continuous quantitative variables. These values run along a scale. Discrete values have limitations, but continuous variables are often measured into decimals. Any value within possible limits can be obtained when measuring the height of the football players, and the heights can be measured down to 1/16th of an inch, if not further.

Statisticians can hold various titles and positions within a company. The average total compensation for a statistician with one to three years of experience was $81,885 as of December 2023. This increased to $109,288 with 15 years of experience.

Statistical Levels of Measurement

There are several resulting levels of measurement after analyzing variables and outcomes. Statistics can quantify outcomes in four ways.

Nominal-level Measurement

There’s no numerical or quantitative value, and qualities are not ranked. Nominal-level measurements are instead simply labels or categories assigned to other variables. It’s easiest to think of nominal-level measurements as non-numerical facts about a variable.

Example : The name of the U.S. president elected in 2020 was Joseph Robinette Biden Jr.

Ordinal-level Measurement

Outcomes can be arranged in an order, but all data values have the same value or weight. Although they’re numerical, ordinal-level measurements can’t be subtracted against each other in statistics because only the position of the data point matters. Ordinal levels are often incorporated into nonparametric statistics and compared against the total variable group.

Example : American Fred Kerley was the second-fastest man at the 2020 Tokyo Olympics based on 100-meter sprint times.

Interval-level Measurement

Outcomes can be arranged in order, but differences between data values may now have meaning. Two data points are often used to compare the passing of time or changing conditions within a data set. There is often no “starting point” for the range of data values, and calendar dates or temperatures may not have a meaningful intrinsic zero value.

Example : Inflation hit 8.6% in May 2022. The last time inflation was that high was in December 1981 .

Ratio-level Measurement

Outcomes can be arranged in order, and differences between data values now have meaning. But there’s a starting point or “zero value” that can be used to further provide value to a statistical value. The ratio between data values has meaning, including its distance away from zero.

Example : The lowest meteorological temperature recorded was -128.6 degrees Fahrenheit in Antarctica in 1983.

Statistics Sampling Techniques

Often, it's not possible to gather data from every data point within a population to gather statistical information. Statistics relies instead on different sampling techniques to create a representative subset of the population that’s easier to analyze. In statistics, there are several primary types of sampling.

Simple Random Sampling

Simple random sampling calls for every member within the population to have an equal chance of being selected for analysis. The entire population is used as the basis for sampling, and any random generator based on chance can select the sample items. For example, 100 individuals are lined up and 10 are chosen at random.

Systemic Sampling

Systematic sampling calls for a random sample as well, but its technique is slightly modified to make it easier to conduct. A single random number is generated to determine the starting point, and individuals are then selected at a specified regular interval until the sample size is complete. For example, if 100 individuals are lined up and numbered, and the random starting point is the seventh individual, every subsequent ninth individual (i.e., 7th, 16th, 25th, etc.) is selected until 10 sample items have been selected.

Stratified Sampling

Stratified sampling calls for more control over your sample. The population is divided into subgroups based on similar characteristics. Then you calculate how many people from each subgroup would represent the entire population. For example, 100 individuals are grouped by gender and race. Then a sample from each subgroup is taken in proportion to how representative that subgroup is of the population.

Cluster Sampling

Cluster sampling calls for subgroups as well, but each subgroup should be representative of the population. The entire subgroup is randomly selected instead of randomly selecting individuals within a subgroup.

Not sure which Major League Baseball player should have won Most Valuable Player last year? Statistics, often used to determine value, is often cited when the award for best player is announced. Statistics can include batting average, number of home runs hit, and stolen bases.

Statistics is prominent in finance, investing, business, and a wide scope of sectors. Much of the information you see and the data you’re given is derived from statistics, which are used in all facets of a business.

Statistics in investing include average trading volume, 52-week low, 52-week high, beta, and correlation between asset classes or securities.
Statistics in economics include gross domestic product (GDP), unemployment, consumer pricing, inflation, and other economic growth metrics.
Statistics in marketing include conversion rates, click-through rates, search quantities, and social media metrics.
Statistics in accounting include liquidity, solvency, and profitability metrics across time.
Statistics in information technology include bandwidth, network capabilities, and hardware logistics.
Statistics in human resources include employee turnover, employee satisfaction, and average compensation relative to the market.

Why Is Statistics Important?

Statistics is used to conduct research, evaluate outcomes, develop critical thinking, and make informed decisions about a set of data. Statistics can be used to inquire about almost any field of study to investigate why things happen, when they occur, and whether reoccurrence is predictable.

What’s the Difference Between Descriptive and Inferential Statistics?

Descriptive statistics are used to describe or summarize the characteristics of a sample or data set, such as a variable’s mean, standard deviation, or frequency. Inferential statistics employ any number of techniques to relate variables in a data set to one another. An example would be using correlation or regression analysis. These can then be used to estimate forecasts or infer causality.

Who Uses Statistics?

Statistics are done whenever data are collected and analyzed and used widely across an array of applications and professions. These include government agencies, academic research, investment analysis, and many others.

How Are Statistics Used in Economics and Finance?

Economists collect and look at all sorts of data ranging from consumer spending and housing starts to inflation and GDP growth. In finance, analysts and investors collect data about companies, industries, sentiment, and market data on price and volume. The use of inferential statistics in these fields is known as econometrics. Several important financial models, including the capital asset pricing model (CAPM) , modern portfolio theory (MPT) and the Black-Scholes options pricing model, rely on statistical inference.

Statistics is the practice of analyzing data and drawing inferences from the sample results. Across a variety of fields—from governmental agencies to finance—statistics is used to gather conclusions about a given data set.

The study of statistics can lead to a career as a statistician, but it can also be a handy metric in everyday life. When you’re analyzing the odds that your favorite team will win the Super Bowl before you place a bet, gauging the viability of an investment, or determining whether you’re being comparatively overcharged for a product or service, statistics can be used to gain insights on probable outcomes of objects or events.

Encyclopœdia Britannica. “ Probability and Statistics .”

Coursera. “ How Much Do Statisticians Make? Your 2024 Salary Guide .”

Olympics. “ Tokyo 2020: Athletics Men’s 100m Results .”

U.S. Bureau of Labor Statistics. “ Consumer Price Index .”

Arizona State University, World Meteorological Organization’s World Weather & Climate Extremes Archive. “ World: Lowest Temperature .”

Baseball Reference. “ MLB Most Valuable Player MVP Award Winners .”

Terms of Service
Editorial Policy
Privacy Policy

Have a thesis expert improve your writing

Check your thesis for plagiarism in 10 minutes, generate your apa citations for free.

Knowledge Base

Descriptive Statistics | Definitions, Types, Examples

Published on 4 November 2022 by Pritha Bhandari . Revised on 9 January 2023.

Descriptive statistics summarise and organise characteristics of a data set. A data set is a collection of responses or observations from a sample or entire population .

In quantitative research , after collecting data, the first step of statistical analysis is to describe characteristics of the responses, such as the average of one variable (e.g., age), or the relation between two variables (e.g., age and creativity).

The next step is inferential statistics , which help you decide whether your data confirms or refutes your hypothesis and whether it is generalisable to a larger population.

Types of descriptive statistics, frequency distribution, measures of central tendency, measures of variability, univariate descriptive statistics, bivariate descriptive statistics, frequently asked questions.

There are 3 main types of descriptive statistics:

The distribution concerns the frequency of each value.
The central tendency concerns the averages of the values.
The variability or dispersion concerns how spread out the values are.

You can apply these to assess only one variable at a time, in univariate analysis, or to compare two or more, in bivariate and multivariate analysis.

Go to a library
Watch a movie at a theater
Visit a national park

A data set is made up of a distribution of values, or scores. In tables or graphs, you can summarise the frequency of every possible value of a variable in numbers or percentages.

Simple frequency distribution table
Grouped frequency distribution table

Gender	Number
Male	182
Female	235
Other	27

From this table, you can see that more women than men or people with another gender identity took part in the study. In a grouped frequency distribution, you can group numerical response values and add up the number of responses for each group. You can also convert each of these numbers to percentages.

Library visits in the past year	Percent
0–4	6%
5–8	20%
9–12	42%
13–16	24%
17+	8%

Measures of central tendency estimate the center, or average, of a data set. The mean , median and mode are 3 ways of finding the average.

Here we will demonstrate how to calculate the mean, median, and mode using the first 6 responses of our survey.

The mean , or M , is the most commonly used method for finding the average.

To find the mean, simply add up all response values and divide the sum by the total number of responses. The total number of responses or observations is called N .

Mean number of library visits
Data set	15, 3, 12, 0, 24, 3
Sum of all values	15 + 3 + 12 + 0 + 24 + 3 = 57
Total number of responses	= 6
Mean	Divide the sum of values by to find : 57/6 =

The median is the value that’s exactly in the middle of a data set.

To find the median, order each response value from the smallest to the biggest. Then, the median is the number in the middle. If there are two numbers in the middle, find their mean.

Median number of library visits
Ordered data set	0, 3, 3, 12, 15, 24
Middle numbers	3, 12
Median	Find the mean of the two middle numbers: (3 + 12)/2 =

The mode is the simply the most popular or most frequent response value. A data set can have no mode, one mode, or more than one mode.

To find the mode, order your data set from lowest to highest and find the response that occurs most frequently.

Mode number of library visits
Ordered data set	0, 3, 3, 12, 15, 24
Mode	Find the most frequently occurring response:

Measures of variability give you a sense of how spread out the response values are. The range, standard deviation and variance each reflect different aspects of spread.

The range gives you an idea of how far apart the most extreme response scores are. To find the range , simply subtract the lowest value from the highest value.

Standard deviation

The standard deviation ( s ) is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. The larger the standard deviation, the more variable the data set is.

There are six steps for finding the standard deviation:

List each score and find their mean.
Subtract the mean from each score to get the deviation from the mean.
Square each of these deviations.
Add up all of the squared deviations.
Divide the sum of the squared deviations by N – 1.
Find the square root of the number you found.

Raw data	Deviation from mean	Squared deviation
15	15 – 9.5 = 5.5	30.25
3	3 – 9.5 = -6.5	42.25
12	12 – 9.5 = 2.5	6.25
0	0 – 9.5 = -9.5	90.25
24	24 – 9.5 = 14.5	210.25
3	3 – 9.5 = -6.5	42.25
= 9.5	Sum = 0	Sum of squares = 421.5

Step 5: 421.5/5 = 84.3

Step 6: √84.3 = 9.18

The variance is the average of squared deviations from the mean. Variance reflects the degree of spread in the data set. The more spread the data, the larger the variance is in relation to the mean.

To find the variance, simply square the standard deviation. The symbol for variance is s 2 .

Univariate descriptive statistics focus on only one variable at a time. It’s important to examine data from each variable separately using multiple measures of distribution, central tendency and spread. Programs like SPSS and Excel can be used to easily calculate these.

	Visits to the library
	6
Mean	9.5
Median	7.5
Mode	3
Standard deviation	9.18
Variance	84.3
Range	24

If you were to only consider the mean as a measure of central tendency, your impression of the ‘middle’ of the data set can be skewed by outliers, unlike the median or mode.

Likewise, while the range is sensitive to extreme values, you should also consider the standard deviation and variance to get easily comparable measures of spread.

If you’ve collected data on more than one variable, you can use bivariate or multivariate descriptive statistics to explore whether there are relationships between them.

In bivariate analysis, you simultaneously study the frequency and variability of two variables to see if they vary together. You can also compare the central tendency of the two variables before performing further statistical tests .

Multivariate analysis is the same as bivariate analysis but with more than two variables.

Contingency table

In a contingency table, each cell represents the intersection of two variables. Usually, an independent variable (e.g., gender) appears along the vertical axis and a dependent one appears along the horizontal axis (e.g., activities). You read ‘across’ the table to see how the independent and dependent variables relate to each other.

	Number of visits to the library in the past year
Group	0–4	5–8	9–12	13–16	17+
Children	32	68	37	23	22
Adults	36	48	43	83	25

Interpreting a contingency table is easier when the raw data is converted to percentages. Percentages make each row comparable to the other by making it seem as if each group had only 100 observations or participants. When creating a percentage-based contingency table, you add the N for each independent variable on the end.

	Visits to the library in the past year (Percentages)
Group	0–4	5–8	9–12	13–16	17+
Children	18%	37%	20%	13%	12%	182
Adults	15%	20%	18%	35%	11%	235

From this table, it is more clear that similar proportions of children and adults go to the library over 17 times a year. Additionally, children most commonly went to the library between 5 and 8 times, while for adults, this number was between 13 and 16.

Scatter plots

A scatter plot is a chart that shows you the relationship between two or three variables. It’s a visual representation of the strength of a relationship.

In a scatter plot, you plot one variable along the x-axis and another one along the y-axis. Each data point is represented by a point in the chart.

From your scatter plot, you see that as the number of movies seen at movie theaters increases, the number of visits to the library decreases. Based on your visual assessment of a possible linear relationship, you perform further tests of correlation and regression.

Descriptive statistics summarise the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalisable to the broader population.

The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset.

Distribution refers to the frequencies of different responses.
Measures of central tendency give you the average for each response.
Measures of variability show you the spread or dispersion of your dataset.
Univariate statistics summarise only one variable at a time.
Bivariate statistics compare two variables .
Multivariate statistics compare more than two variables .

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

Bhandari, P. (2023, January 09). Descriptive Statistics | Definitions, Types, Examples. Scribbr. Retrieved 21 August 2024, from https://www.scribbr.co.uk/stats/descriptive-statistics-explained/

Is this article helpful?

Pritha Bhandari

Other students also liked, data collection methods | step-by-step guide & examples, variability | calculating range, iqr, variance, standard deviation, normal distribution | examples, formulas, & uses.

Random Sampling vs. Random Assignment

Random sampling and random assignment are fundamental concepts in the realm of research methods and statistics. However, many students struggle to differentiate between these two concepts, and very often use these terms interchangeably. Here we will explain the distinction between random sampling and random assignment.

Random sampling refers to the method you use to select individuals from the population to participate in your study. In other words, random sampling means that you are randomly selecting individuals from the population to participate in your study. This type of sampling is typically done to help ensure the representativeness of the sample (i.e., external validity). It is worth noting that a sample is only truly random if all individuals in the population have an equal probability of being selected to participate in the study. In practice, very few research studies use “true” random sampling because it is usually not feasible to ensure that all individuals in the population have an equal chance of being selected. For this reason, it is especially important to avoid using the term “random sample” if your study uses a nonprobability sampling method (such as convenience sampling).

Discover How We Assist to Edit Your Dissertation Chapters

Aligning theoretical framework, gathering articles, synthesizing gaps, articulating a clear methodology and data plan, and writing about the theoretical and practical implications of your research are part of our comprehensive dissertation editing services.

Bring dissertation editing expertise to chapters 1-5 in timely manner.
Track all changes, then work with you to bring about scholarly writing.
Ongoing support to address committee feedback, reducing revisions.

Random assignment refers to the method you use to place participants into groups in an experimental study. For example, say you are conducting a study comparing the blood pressure of patients after taking aspirin or a placebo. You have two groups of patients to compare: patients who will take aspirin (the experimental group) and patients who will take the placebo (the control group). Ideally, you would want to randomly assign the participants to be in the experimental group or the control group, meaning that each participant has an equal probability of being placed in the experimental or control group. This helps ensure that there are no systematic differences between the groups before the treatment (e.g., the aspirin or placebo) is given to the participants. Random assignment is a fundamental part of a “true” experiment because it helps ensure that any differences found between the groups are attributable to the treatment, rather than a confounding variable.

So, to summarize, random sampling refers to how you select individuals from the population to participate in your study. Random assignment refers to how you place those participants into groups (such as experimental vs. control). Knowing this distinction will help you clearly and accurately describe the methods you use to collect your data and conduct your study.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

Knowledge Base
Inferential Statistics | An Easy Introduction & Examples

Inferential Statistics | An Easy Introduction & Examples

Published on September 4, 2020 by Pritha Bhandari . Revised on June 22, 2023.

While descriptive statistics summarize the characteristics of a data set, inferential statistics help you come to conclusions and make predictions based on your data.

When you have collected data from a sample , you can use inferential statistics to understand the larger population from which the sample is taken.

Inferential statistics have two main uses:

making estimates about populations (for example, the mean SAT score of all 11th graders in the US).
testing hypotheses to draw conclusions about populations (for example, the relationship between SAT scores and family income).

Descriptive versus inferential statistics, estimating population parameters from sample statistics, hypothesis testing, other interesting articles, frequently asked questions about inferential statistics.

Descriptive statistics allow you to describe a data set, while inferential statistics allow you to make inferences based on a data set.

Descriptive statistics

Using descriptive statistics, you can report characteristics of your data:

The distribution concerns the frequency of each value.
The central tendency concerns the averages of the values.
The variability concerns how spread out the values are.

In descriptive statistics, there is no uncertainty – the statistics precisely describe the data that you collected. If you collect data from an entire population, you can directly compare these descriptive statistics to those from other populations.

Inferential statistics

Most of the time, you can only acquire data from samples, because it is too difficult or expensive to collect data from the whole population that you’re interested in.

While descriptive statistics can only summarize a sample’s characteristics, inferential statistics use your sample to make reasonable guesses about the larger population.

With inferential statistics, it’s important to use random and unbiased sampling methods . If your sample isn’t representative of your population, then you can’t make valid statistical inferences or generalize .

Sampling error in inferential statistics

Since the size of a sample is always smaller than the size of the population, some of the population isn’t captured by sample data. This creates sampling error , which is the difference between the true population values (called parameters) and the measured sample values (called statistics).

Sampling error arises any time you use a sample, even if your sample is random and unbiased. For this reason, there is always some uncertainty in inferential statistics. However, using probability sampling methods reduces this uncertainty.

Prevent plagiarism. Run a free check.

The characteristics of samples and populations are described by numbers called statistics and parameters :

A statistic is a measure that describes the sample (e.g., sample mean ).
A parameter is a measure that describes the whole population (e.g., population mean).

Sampling error is the difference between a parameter and a corresponding statistic. Since in most cases you don’t know the real population parameter, you can use inferential statistics to estimate these parameters in a way that takes sampling error into account.

There are two important types of estimates you can make about the population: point estimates and interval estimates .

A point estimate is a single value estimate of a parameter. For instance, a sample mean is a point estimate of a population mean.
An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.

Both types of estimates are important for gathering a clear idea of where a parameter is likely to lie.

Confidence intervals

A confidence interval uses the variability around a statistic to come up with an interval estimate for a parameter. Confidence intervals are useful for estimating parameters because they take sampling error into account.

While a point estimate gives you a precise value for the parameter you are interested in, a confidence interval tells you the uncertainty of the point estimate. They are best used in combination with each other.

Each confidence interval is associated with a confidence level. A confidence level tells you the probability (in percentage) of the interval containing the parameter estimate if you repeat the study again.

A 95% confidence interval means that if you repeat your study with a new sample in exactly the same way 100 times, you can expect your estimate to lie within the specified range of values 95 times.

Although you can say that your estimate will lie within the interval a certain percentage of the time, you cannot say for sure that the actual population parameter will. That’s because you can’t know the true value of the population parameter without collecting data from the full population.

However, with random sampling and a suitable sample size, you can reasonably expect your confidence interval to contain the parameter a certain percentage of the time.

Your point estimate of the population mean paid vacation days is the sample mean of 19 paid vacation days.

Hypothesis testing is a formal process of statistical analysis using inferential statistics. The goal of hypothesis testing is to compare populations or assess relationships between variables using samples.

Hypotheses , or predictions, are tested using statistical tests . Statistical tests also estimate sampling errors so that valid inferences can be made.

Statistical tests can be parametric or non-parametric. Parametric tests are considered more statistically powerful because they are more likely to detect an effect if one exists.

Parametric tests make assumptions that include the following:

the population that the sample comes from follows a normal distribution of scores
the sample size is large enough to represent the population
the variances , a measure of variability , of each group being compared are similar

When your data violates any of these assumptions, non-parametric tests are more suitable. Non-parametric tests are called “distribution-free tests” because they don’t assume anything about the distribution of the population data.

Statistical tests come in three forms: tests of comparison, correlation or regression.

Comparison tests

Comparison tests assess whether there are differences in means, medians or rankings of scores of two or more groups.

To decide which test suits your aim, consider whether your data meets the conditions necessary for parametric tests, the number of samples, and the levels of measurement of your variables.

Means can only be found for interval or ratio data , while medians and rankings are more appropriate measures for ordinal data .


test	Yes	Means	2 samples
	Yes	Means	3+ samples
Mood’s median	No	Medians	2+ samples
Wilcoxon signed-rank	No	Distributions	2 samples
Wilcoxon rank-sum (Mann-Whitney )	No	Sums of rankings	2 samples
Kruskal-Wallis	No	Mean rankings	3+ samples

Correlation tests

Correlation tests determine the extent to which two variables are associated.

Although Pearson’s r is the most statistically powerful test, Spearman’s r is appropriate for interval and ratio variables when the data doesn’t follow a normal distribution.

The chi square test of independence is the only test that can be used with nominal variables.


Pearson’s	Yes	Interval/ratio variables
Spearman’s	No	Ordinal/interval/ratio variables
Chi square test of independence	No	Nominal/ordinal variables

Regression tests

Regression tests demonstrate whether changes in predictor variables cause changes in an outcome variable. You can decide which regression test to use based on the number and types of variables you have as predictors and outcomes.

Most of the commonly used regression tests are parametric. If your data is not normally distributed, you can perform data transformations.

Data transformations help you make your data normally distributed using mathematical operations, like taking the square root of each value.


	1 interval/ratio variable	1 interval/ratio variable
	2+ interval/ratio variable(s)	1 interval/ratio variable
Logistic regression	1+ any variable(s)	1 binary variable
Nominal regression	1+ any variable(s)	1 nominal variable
Ordinal regression	1+ any variable(s)	1 ordinal variable

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

Confidence interval
Measures of central tendency
Correlation coefficient

Methodology

Cluster sampling
Stratified sampling
Types of interviews
Cohort study
Thematic analysis

Research bias

Implicit bias
Cognitive bias
Survivorship bias
Availability heuristic
Nonresponse bias
Regression to the mean

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

Academic style
Vague sentences
Style consistency

See an example

Descriptive statistics summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalizable to the broader population.

A statistic refers to measures about the sample , while a parameter refers to measures about the population .

A sampling error is the difference between a population parameter and a sample statistic .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Bhandari, P. (2023, June 22). Inferential Statistics | An Easy Introduction & Examples. Scribbr. Retrieved August 21, 2024, from https://www.scribbr.com/statistics/inferential-statistics/

Is this article helpful?

Pritha Bhandari

Other students also liked, parameter vs statistic | definitions, differences & examples, descriptive statistics | definitions, types, examples, hypothesis testing | a step-by-step guide with easy examples, what is your plagiarism score.

Math Article

Probability And Statistics

Probability And Statistics are the two important concepts in Maths. Probability is all about chance. Whereas statistics is more about how we handle various data using different techniques. It helps to represent complicated data in a very easy and understandable way. Statistics and probability are usually introduced in Class 10, Class 11 and Class 12 students are preparing for school exams and competitive examinations. The introduction of these fundamentals is briefly given in your academic books and notes. The statistic has a huge application nowadays in data science professions. The professionals use the stats and do the predictions of the business. It helps them to predict the future profit or loss attained by the company.

Table of contents:

Probability
Probability Topics
Statistics Topics

Solved Examples

What is probability.

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen. For example, when we flip a coin in the air, what is the possibility of getting a head ? The answer to this question is based on the number of possible outcomes. Here the possibility is either head or tail will be the outcome. So, the probability of a head to come as a result is 1/2.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

P(E) = n(E)/n(S)

n(E) = Number of event favourable to event E

n(S) = Total number of outcomes

What is Statistics?

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. It is a method of collecting and summarising the data. This has many applications from a small scale to large scale. Whether it is the study of the population of the country or its economy, stats are used for all such data analysis.

Statistics has a huge scope in many fields such as sociology, psychology, geology, weather forecasting, etc. The data collected here for analysis could be quantitative or qualitative. Quantitative data are also of two types such as: discrete and continuous. Discrete data has a fixed value whereas continuous data is not a fixed data but has a range. There are many terms and formulas used in this concept. See the below table to understand them .

Terms Used in Probability and Statistics

There are various terms utilised in the probability and statistics concepts, Such as:

Random Experiment

Sample Sample
Random variables

Expected Value

Independence

Let us discuss these terms one by one.

An experiment whose result cannot be predicted, until it is noticed is called a random experiment. For example, when we throw a dice randomly, the result is uncertain to us. We can get any output between 1 to 6. Hence, this experiment is random.

Sample Space

A sample space is the set of all possible results or outcomes of a random experiment. Suppose, if we have thrown a dice, randomly, then the sample space for this experiment will be all possible outcomes of throwing a dice, such as;

Sample Space = { 1,2,3,4,5,6}

Random Variables

The variables which denote the possible outcomes of a random experiment are called random variables. They are of two types:

Discrete Random Variables
Continuous Random Variables

Discrete random variables take only those distinct values which are countable. Whereas continuous random variables could take an infinite number of possible values.

Independent Event

When the probability of occurrence of one event has no impact on the probability of another event, then both the events are termed as independent of each other. For example, if you flip a coin and at the same time you throw a dice, the probability of getting a ‘head’ is independent of the probability of getting a 6 in dice.

Mean of a random variable is the average of the random values of the possible outcomes of a random experiment. In simple terms, it is the expectation of the possible outcomes of the random experiment, repeated again and again or n number of times. It is also called the expectation of a random variable.

Expected value is the mean of a random variable. It is the assumed value which is considered for a random experiment. It is also called expectation, mathematical expectation or first moment. For example, if we roll a dice having six faces, then the expected value will be the average value of all the possible outcomes, i.e. 3.5.

Basically, the variance tells us how the values of the random variable are spread around the mean value. It specifies the distribution of the sample space across the mean.

List of Probability Topics

Basic probability topics are :

Addition Rule of Probability	Binomial Probability
Compound Events	Compound Probability	Complementary Events
	Complementary Events	Coin Toss Probability
		Geometric Probability

Properties of Probability	Probability Line	Probability without Replacement
	Simple Event

List of Statistical Topics

Basic Statistics topics are:

Box and Whisker Plots	Comparing Two Means	Comparing Two Proportions

	Degree of freedom	Empirical Rule
	Five Number Summary

	Data Range
	Scatter Plots
Ungrouped Data

Probability and Statistics Formulas

Probability Formulas : For two events A and B:

Probability Range	Probability of an event ranges from 0 to 1 i.e. 0 ≤ P(A) ≤ 1
Rule of Complementary Events	P(A’) + P(A) = 1
Rule of Addition	P(A∪B) = P(A) + P(B) – P(A∩B)
Mutually Exclusive Events	P(A∪B) = P(A) + P(B)
Independent Events	P(A∩B) = P(A)P(B)
Disjoint Events	P(A∩B) = 0
Conditional Probability	P(A\|B) = P(A∩B)/P(B)
Bayes Formula	P(A\|B) = P(B\|A) P(A)/P(B)

Statistics Formulas : Some important formulas are listed below:

Let x be an item given and n is the total number of items.

Mean	Mean = (Sum of all the terms)/(Total number of terms)
Median
Mode	The most frequently occurring value
Standard Deviation
Variance

Here are some examples based on the concepts of statistics and probability to understand better. Students can practice more questions based on these solved examples to excel in the topic. Also, make use of the formulas given in this article in the above section to solve problems based on them.

Example 1 : Find the mean and mode of the following data: 2, 3, 5, 6, 10, 6, 12, 6, 3, 4.

Total Count: 10

Sum of all the numbers: 2+3+5+6+10+6+12+6+3+7=60

Mean = (sum of all the numbers)/(Total number of items)

Mean = 60/10 = 6

Again, Number 6 is occurring for 3 times, therefore Mode = 6. Answer

Example 2: A bucket contains 5 blue, 4 green and 5 red balls. Sudheer is asked to pick 2 balls randomly from the bucket without replacement and then one more ball is to be picked. What is the probability he picked 2 green balls and 1 blue ball?

Solution : Total number of balls = 14

Probability of drawing

1 green ball = 4/14

another green ball = 3/13

1 blue ball = 5/12

Probability of picking 2 green balls and 1 blue ball = 4/14 * 3/13 * 5/12 = 5/182.

Example 3 : What is the probability that Ram will choose a marble at random and that it is not black if the bowl contains 3 red, 2 black and 5 green marbles.

Solution : Total number of marble = 10

Red and Green marbles = 8

Find the number of marbles that are not black and divide by the total number of marbles.

So P(not black) = (number of red or green marbles)/(total number of marbles)

Example 4: Find the mean of the following data:

55, 36, 95, 73, 60, 42, 25, 78, 75, 62

Solution: Given,

55 36 95 73 60 42 25 78 75 62

Sum of observations = 55 + 36 + 95 + 73 + 60 + 42 + 25 + 78 + 75 + 62 = 601

Number of observations = 10

Mean = 601/10 = 60.1

Example 5: Find the median and mode of the following marks (out of 10) obtained by 20 students:

4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9

Ascending order: 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 9, 9, 9, 9, 10, 10

Number of observations = n = 20

Median = (10th + 11th observation)/2

= (6 + 6)/2

Most frequent observations = 9

Hence, the mode is 9.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Maths related queries and study materials

Your result is as below

Request OTP on Voice Call

MATHS Related Links

Register with BYJU'S & Download Free PDFs

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

Authors: Barbara Illowsky, Susan Dean
Publisher/website: OpenStax
Book title: Statistics
Publication date: Mar 27, 2020
Location: Houston, Texas
Book URL: https://openstax.org/books/statistics/pages/1-introduction
Section URL: https://openstax.org/books/statistics/pages/1-key-terms

© Apr 16, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Faculty Resources

Assignments.

The assignments for Concepts in Statistics are typically centered around a dataset that the student uses in conjunction with a statistics package. The activity has the student explore the dataset, generate descriptive statistics and appropriate graphs from the data, and interpret the output. Instructions are provided for five different statistics packages:

TI Calculator

If you import this course into your learning management system (Blackboard, Canvas, etc.), the assignments will automatically be loaded into the assignment tool. They can be used as is, modified, or removed. You can preview them below:

Assignments and Alignment
Assignment	Module
	Module 2: Summarizing Data Graphically and Numerically
	Module 2: Summarizing Data Graphically and Numerically
	Module 2: Summarizing Data Graphically and Numerically
	Module 2: Summarizing Data Graphically and Numerically
	Module 2: Summarizing Data Graphically and Numerically
	Module 3: Examining Relationships: Quantitative Data
	Module 3: Examining Relationships: Quantitative Data
	Module 3: Examining Relationships: Quantitative Data
	Module 3: Examining Relationships: Quantitative Data
	Module 8: Inference for One Proportion
	Module 9: Inference for Two Proportions
	Module 10: Inference for Means
	Module 10: Inference for Means
	Module 10: Inference for Means
	Module 10: Inference for Means
	Module 10: Inference for Means
	Module 10: Inference for Means
	Module 10: Inference for Means
	Module 11: Chi-Square Tests

Contribute!

Improve this page Learn More

Assignments. Provided by : Lumen Learning. License : CC BY: Attribution
Pencil Cup. Authored by : IconfactoryTeam. Provided by : Noun Project. Located at : https://thenounproject.com/term/pencil-cup/628840/ . License : CC BY: Attribution

Official websites use .gov

A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS

A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Births in the United States, 2023

NCHS Data Brief No. 507, August 2024

PDF Version (454 KB)

Joyce A. Martin, M.P.H., Brady E. Hamilton Ph.D., and Michelle J.K. Osterman, M.H.S.

Key findings

The number of births and the general fertility rate declined from 2022 to 2023.

Birth rates declined for females ages 15–19 from 2022 to 2023., prenatal care beginning in the first trimester declined for the second year in a row in 2023., the preterm birth rate was unchanged from 2022 to 2023, but early-term births increased., data source and methods, about the authors, suggested citation.

Data from the National Vital Statistics System

The number of births in the United States declined 2% from 2022 to 2023. The general fertility rate declined 3% in 2023 to 54.5 births per 1,000 females ages 15–44.
Birth rates declined for females ages 15–19 (4%), 15–17 (2%), and 18–19 (5%), from 2022 to 2023.
The percentage of mothers receiving prenatal care in the first trimester of pregnancy declined 1% from 2022 to 2023, while the percentage of mothers with no prenatal care increased 5%.
The preterm birth rate was essentially unchanged at 10.41% in 2023, but the rate of early-term births rose 2% to 29.84%.

This report presents highlights from 2023 final birth data on key demographic and maternal and infant health indicators. The number of births, the general fertility rate (births per 1,000 females ages 15–44), teen birth rates, the distribution of births by trimester prenatal care began, and the distribution of births by gestational age (less than 37 weeks, 37–38 weeks, 39–40 weeks, and 41 or later weeks of gestation) are presented. For all indicators, results for 2023 are compared with those for 2022 and 2021.

Keywords : general fertility rate, prenatal care, gestational age, National Vital Statistics System.

In 2023, 3,596,017 births were registered in the United States, down 2% from 2022 (3,667,758) and 2021 (3,664,292) ( Figure 1 , Table 1 ).
The general fertility rate for the United States decreased 3% in 2023 to 54.5 births per 1,000 females ages 15–44 from 56.0 in 2022; the general fertility rate was also down 3% from 2021 (56.3).

Figure 1. Number of live births and general fertility rates: United States, 2021–2023

Table 1
Year	Births	Fertility rate
2021	3,664,292	56.3
2022	3,667,758	56.0
2023	3,596,017	54.5

NOTES: General fertility rates are births per 1,000 women ages 15–44. Rates are based on population estimates as of July 1 for 2021, 2022, and 2023. SOURCE: National Center for Health Statistics, National Vital Statistics System, natality data file.

The birth rate for teenagers ages 15–19 declined 4% from 2022 to 2023, from 13.6 to 13.1 births per 1,000 females, and was down 6% from 2021 (13.9) ( Figure 2 , Table 2 ).
From 2022 to 2023, the birth rate for teenagers ages 15–17 declined 2%, from 5.6 to 5.5; there was no change in the rate from 2021 to 2022.
The rate for teenagers ages 18–19 declined 5% from 2022 to 2023, from 25.8 to 24.6 and has declined 8% since 2021 (26.6).

Figure 2. Birth rate for teenagers, by maternal age: United States, 2021–2023



	Maternal age
Year	15–19	15–17	18–19
	Percentage
2002	13.9	5.6	26.6
2003	13.6	5.6	25.8
2004	13.1	5.5	24.6

NOTES: Age-specific birth rates are births per 1,000 females in specified age group. Rates are based on population estimates as of July 1 for each year 2021–2023. SOURCE: National Center for Health Statistics, National Vital Statistics System, natality data file.

Prenatal care beginning in the first trimester declined 1% in 2023 to 76.1%, from 77.0% in 2022. This follows a 2% decline from 2021 (78.3%) to 2022 ( Figure 3 , Table 3 ).
Care beginning in the second trimester increased 4% in 2023, from 16.3% in 2022 to 16.9%. This follows a 6% increase from 2021 (15.4%).
Care beginning in the third trimester increased 2% from 2022 (4.6%) to 2023 (4.7%) following a 10% increase from 2021 (4.2%) to 2022.
The percentage of mothers receiving no prenatal care increased 5% in 2023 to 2.3% from 2.2% in 2022; the percentage of mothers with no prenatal care also rose 5% from 2021 (2.1%) to 2022.

Figure 3. Distribution of trimester prenatal care began: United States, 2021–2023


Trimester
Trimester	2021	2022	2023
	Percentage
First trimester	78.3	77.0	76.1
Second trimester	15.4	16.3	16.9
Third trimester	4.2	4.6	4.7
No care	2.1	2.2	2.3

SOURCE: National Center for Health Statistics, National Vital Statistics System, natality data file.

The percentage of infants born preterm was essentially unchanged from 2022 (10.38%) to 2023 (10.41%) but was down 1% from 2021 (10.49%) ( Figure 4 , Table 4 ).
The percentage of infants born early term rose 2% from 2022 to 2023, from 29.31% to 29.84%, and was up 4% from 2021 (28.76%).
In contrast, the percentage of full-term births declined 1%, from 2022 to 2023 (55.32% to 54.94%) and has declined 2% since 2021 (55.90%).
The percentage of infants born late or post term was 4.82% in 2023, down 3% from 2022 (4.99%) and 1% from 2021 (4.85%).

Figure 4. Distribution of births by gestational age: United States, 2021–2023



	Gestational age
Year	Preterm	Early term	Full term	Late and post term
	Percentage
2021	10.49	28.76	55.9	4.85
2022	10.38	29.31	55.32	4.99
2023	10.41	29.84	54.94	4.82

NOTES: Preterm is less than 37 weeks, early term is 37 to 38 weeks, full term is 39 to 40 weeks, and late and post-term is 41 weeks or more. Source: National Center for Health Statistics, National Vital Statistics System, natality data file. SOURCE: National Center for Health Statistics, National Vital Statistics System, natality data file.

U.S. birth certificate data for 2023 show continued declines in the number (2%) and rate (3%) of births from 2022 to 2023. Since the most recent high in 2007, the number of births has declined 17%, and the general fertility rate has declined 21% ( 1 ). The teen birth rate also continued to decline in 2023 and has declined two-thirds since 2007 ( 1 ). The percentage of women beginning care in the first trimester of pregnancy declined in 2023 and was down 3% from the most recent high in 2021; first trimester care had been on the rise from 2016 to 2021. At the same time, the percentage of women with late care or with no care rose from 2021 to 2023; late and no-care levels have risen steadily since 2016 ( 1 ). The preterm birth rate was essentially unchanged from 2022 to 2023, but early-term births rose 2%, and full-term and late- and post-term births declined 1% and 3%, respectively. Since the most recent low in 2014, preterm birth rates have risen 9% and early-term births by 21%, while full-term and late- and post-term births have declined ( 1 ).

General fertility rate : Number of births per 1,000 females ages 15–44.

Gestational age : Preterm is births delivered before 37 completed weeks of gestation, early term is 37–38 weeks, full term is 39–40 weeks, and late and post term is 41 or later weeks. Gestational age is based on the obstetric estimate of gestation in completed weeks.

Teenage birth rates : Births per 1,000 females in the specified age groups 15–19, 15–17, and 18–19.

Trimester prenatal care began : The timing of care based on the date a physician or other health care provider examined or counseled the pregnant woman for the pregnancy and the obstetric estimate of gestational age.

This report uses data from the natality data file from the National Vital Statistics System. The vital statistics natality file is based on information from birth certificates and includes information for all births occurring in the United States. This Data Brief accompanies the release of the 2023 natality public-use file ( 2 ). More detailed analyses of the topics presented in this report and other topics such as births by age of mother, tobacco use during pregnancy, pregnancy risk factors, prenatal care timing and utilization, receipt of WIC food, maternal body mass index, and breastfeeding are possible by using the annual natality files ( 2 ). Additional information from the 2023 final birth data file is available via the CDC WONDER platform and will be included in the final 2023 National Vital Statistics Births Report.

References to increases or decreases in rates or percentages indicate differences are statistically significant at the 0.05 level based on a two-tailed z test. References to decreases in the number of births indicate differences are statistically significant at the 0.05 level based on a two-tailed chi-squared test. Computations exclude records for which information is unknown.

Rates shown in this report are based on population estimates calculated from a base that incorporates the 2020 census, vintage 2020 estimates for April 1, 2020, and 2020 demographic analysis estimates. Rates are calculated based on population estimates as of July 1, 2022, (vintage 2022) and July 1, 2023 (vintage 2023) ( 1 , 3 ). The vintage 2023 population estimates include methodological changes made after the release of the vintage 2022 population estimates and projection ( 4 , 5 ). Changes in rates from 2022 to 2023 reflect changes in births and changes in population estimates.

Joyce A. Martin, Brady E. Hamilton, and Michelle J.K. Osterman are with the National Center for Health Statistics, Division of Vital Statistics.

Osterman MJK, Hamilton BE, Martin JA, Driscoll AK, Valenzuela CP. Births: Final data for 2022. National Vital Statistics Reports; vol 73 no 1. Hyattsville, MD: National Center for Health Statistics. 2024. DOI: https://dx.doi.org/10.15620/cdc:145588
National Center for Health Statistics. Vital statistics online data portal .
U.S. Census Bureau. Annual state resident population estimates for six race groups (five race alone groups and two or more races) by age, sex, and Hispanic origin: April 1, 2010, to July 1, 2023 . 2024.
U.S. Census Bureau. Methodology for the United States population estimates: Vintage 2023 . Nation, states, counties, and Puerto Rico—April 1, 2010 to July 1, 2023. 2023.
U.S. Census Bureau. Vintage 2023 release notes . 2024.

Martin JA, Hamilton BE, Osterman MJK. Births in the United States, 2023. NCHS Data Brief, no 507. Hyattsville, MD: National Center for Health Statistics. 2024. DOI: https://dx.doi.org/10.15620/cdc/158789 .

Copyright information

All material appearing in this report is in the public domain and may be reproduced or copied without permission; citation as to source, however, is appreciated.

National Center for Health Statistics

Brian C. Moyer, Ph.D., Acting Director Amy M. Branum, Ph.D., Associate Director for Science

Division of Vital Statistics

Paul D. Sutton, Ph.D., Acting Director Andrés A. Berruti, Ph.D., M.A., Associate Director for Science

Get E-mail Updates
Data Visualization Gallery
NHIS Early Release Program
MMWR QuickStats
Government Printing Office Bookstore

Cookies on GOV.UK

We use some essential cookies to make this website work.

We’d like to set additional cookies to understand how you use GOV.UK, remember your settings and improve government services.

We also use cookies set by other sites to help us deliver content from their services.

You have accepted additional cookies. You can change your cookie settings at any time.

You have rejected additional cookies. You can change your cookie settings at any time.

Scottish VAT Assignment Experimental Statistics 2022

This release of experimental statistics on Scottish VAT assignment will include the 2022 estimate and further historical estimates in the back series.  The VAT assignment model calculates the Scottish share of UK VAT for the purposes of Scottish VAT assignment.  This release will be published at 9:30am on 26 September 2024.  If you have any further queries, please contact:  [email protected]

Is this page useful?

Yes this page is useful
No this page is not useful

Help us improve GOV.UK

Don’t include personal or financial information like your National Insurance number or credit card details.

To help us improve GOV.UK, we’d like to know more about your visit today. Please fill in this survey (opens in a new tab) .

New Hampshire
North Carolina
Pennsylvania
West Virginia
Online hoaxes
Coronavirus
Health Care
Immigration
Environment
Foreign Policy
Kamala Harris
Donald Trump
Mitch McConnell
Hakeem Jeffries
Ron DeSantis
Tucker Carlson
Sean Hannity
Rachel Maddow
PolitiFact Videos
2024 Elections
Mostly True
Mostly False
Pants on Fire
Biden Promise Tracker
Trump-O-Meter
Latest Promises
Our Process
Who pays for PolitiFact?
Advertise with Us
Suggest a Fact-check
Corrections and Updates
Newsletters

Stand up for the facts!

Our only agenda is to publish the truth so you can be an informed participant in democracy. We need your help.

I would like to contribute

Fact-checking dnc night 2: what democratic speakers got right, wrong.

Read in Español

Former President Barack Obama speaks Aug. 20, 2024, at the Democratic National Convention in Chicago. (AP)

CHICAGO — Two decades after exploding onto the political scene at a different Democratic convention, former President Barack Obama, along with former first lady Michelle Obama, energized convention attendees here. The Obamas bestowed their support on nominee Kamala Harris, who aims to follow Barack Obama as the nation’s second Black president.

Barack Obama began his address by praising outgoing President Joe Biden. "I am proud to call him my president, but I am even prouder to call him my friend," Obama said of Biden, his former vice president.

Obama attacked Harris’ opponent, former President Donald Trump with zingers, once needling Trump for a " weird obsession with crowd sizes " (which also involved a suggestive hand gesture).

Barack Obama offered a few notes that rhymed with his career-making 2004 keynote address at the Democratic convention in Boston, in which he argued against the idea that there is a blue America and a red America.

Michelle Obama’s speech also offered some optimistic notes, including the notion that "hope is making a comeback" with Harris’ late entry into the presidential race as Biden’s would-be successor. But the former first lady’s remarks were sometimes even more acerbic than her husband’s.

She said, for example, that Trump had benefited from the "affirmative action of generational wealth" yet still managed to get "a second, third or fourth chance" while regularly "whining" or "cheating." She also criticized Trump — an early spreader of the "birther" conspiracy theory that doubted that Obama was born in the U.S. — for having made Americans "fear us" as an educated, high-achieving couple who "happen to be Black."

PolitiFact fact-checks politicians across the political spectrum. We also fact-checked the Republican National Convention in July. Read more about our process.

Here are some fact-checks of claims made during the convention’s second night.

Barack Obama: Under Joe Biden, the U.S. produced "15 million jobs, higher wages, lower health care costs."

He’s right about jobs: The U.S. has added 15.8 million jobs since January 2021, when Biden was sworn in, though some of those represented the workforce return of workers the pandemic had sidelined.

Wages are up under Biden without factoring in inflation. But for his full tenure, wages have trailed inflation , which hit a four-decade high under Biden. Nevertheless, wages have outpaced inflation over the past two years, the past year and compared with before the pandemic.

Whether health care costs were lower overall is a trickier question, because there’s great variation from family to family and person to person. However, U.S. health care expenditures as a percentage of gross domestic product peaked during the pandemic in 2020 and have since fallen roughly to prepandemic levels. This represented the biggest sustained decline in decades.

LIVE BLOG: Explore PolitiFact’s live fact-checking feed from Night 2 of DNC 2024

Sen. Bernie Sanders, I-Vt.: "Unemployment was soaring" when Biden and Harris took office in January 2021.

Mostly False.

Sanders overstated the unemployment situation that existed when Biden and Harris were inaugurated.

In April 2020, at the start of the COVID-19 pandemic, the unemployment rate surged to 14.8% as millions of Americans lost their jobs.

But by the time Biden took office in January 2021, the rate had fallen to 6.4%, and it continued to fall that year. So it wasn’t "soaring" any longer, though the rate was still high by historical standards. It was lower than 6.4% for about six years prepandemic.

July’s unemployment rate is 4.3%.

Pennsylvania state Rep. Malcolm Kenyatta, D-Philadelphia: "And on Page 587, Project 2025 would cut overtime pay for hardworking Americans."

Labor law experts have told PolitiFact that the Project 2025 plan would not eliminate overtime pay, but some workers could lose overtime protections if the plan’s proposals are enacted. It’s hard to say how many; it would depend on what’s enacted.

The document proposes that the Labor Department maintain an overtime threshold "that does not punish businesses in lower-cost regions (e.g., the southeast United States)." This threshold is the amount of money executive, administrative or professional employees need to make for an employer to exempt them from overtime pay under the Fair Labor Standards Act.

In 2019, the Trump administration finalized a rule that expanded overtime pay eligibility to most salaried workers earning less than about $35,568. The Biden administration raised that threshold to $43,888 beginning July 1, and that will rise to $58,656 on Jan. 1, 2025. Project 2025’s proposal would return to the Trump-era threshold in some parts of the country. It’s unclear how many workers that would affect, but experts said some would presumably lose the right to overtime wages.

Other proposals in the plan include allowing some workers to choose to accumulate paid time off instead of overtime pay, to work more hours in one week and fewer in the next rather than receive overtime and requiring employers to pay overtime for working on the Sabbath.

Former first lady Michelle Obama: One of Trump’s proposals is "shutting down the Department of Education."

Trump has said he would abolish the Education Department , a proposal he shares with Project 2025 , an agenda independently produced by some Trump allies.

It’s also something conservative groups have pushed for decades. The idea is to save a few essential functions and hand them to other agencies.

Trump’s education agenda also includes universal school choice, not spending federal dollars on schools that have vaccine mandates, allowing prayer in school, making principals directly elected by voters, subsidizing homeschooling and abolishing tenure for K-12 teachers.

Sen. Chuck Schumer, D-N.Y.: "Democrats lowered prescription drug prices."

Mostly True.

The Democrats did take historic steps to lower prices for Medicare recipients, but that’s a limited group of people and for many drugs that will take time.

In August 2022, Biden signed the Inflation Reduction Act, which allows the federal government to negotiate prices with drugmakers for Medicare. It passed without Republican support. The same law capped the monthly price of insulin at $35 for Medicare enrollees starting in 2023.

The Biden-Harris administration announced Aug. 15 that the federal government had reached agreements with all participating manufacturers on new negotiated drug prices for the first 10 drugs selected under the new law.

That will define the prices to be paid for prescriptions starting in 2026. For 2027 and 2028, 15 more drugs per year will be chosen for price negotiations. Starting in 2029, 20 more will be chosen a year.

New Mexico Gov. Michelle Lujan Grisham: Donald Trump and J.D. Vance want to "repeal the Affordable Care Act."

Half True .

Trump’s new position doesn’t match his old one, but more details are needed.

In 2016, Trump campaigned on a promise to repeal and replace the Affordable Care Act. As president, Trump supported a failed effort to do just that. In the years since, he has repeatedly stated his intent to dismantle the health care law, including in campaign stops and social media posts throughout 2023.

In March, however, Trump walked back this stance. He wrote on Truth Social that he "isn’t running to terminate" the ACA but to make it "better" and "less expensive."

Trump hasn’t said how he would do this, and health care policy experts said it’s difficult to know where he stands absent a detailed plan. Experts identified an array of possible changes that another Trump administration could execute but said a sweeping repeal likely isn’t in the cards given a lack of political support.

Sanders: "We cut childhood poverty by over 40% through an expanded child tax credit."

Biden’s American Rescue Plan increased the child tax credit from $2,000 to $3,600 for children younger than 6 and to $3,000 for children 6 to 17.

We previously reported that supplemental poverty numbers showed poverty among all U.S. children dropped from 9.7% in 2020 to 5.2% in 2021, the Census Bureau said — a decline of 46%. About 5.3 million people were lifted out of poverty, including 2.9 million children.

The provision lapsed after December 2021, facing opposition from Republicans and Sen. Joe Manchin, now an independent, who argued that expanding the credit would worsen inflation.

When the expanded tax credit expired, supplemental child poverty spiked , rising from 12.1% in December 2021 to 17% in January 2022 — a 41% change.

Kamala Harris in a DNC video: Trump "wants to impose what is in effect a national sales tax on everyday products and basic necessities that we import from other countries. … (it) would cost a typical family $3,900 a year."

Trump has said that he would propose a 10% tariff on all nondomestic goods sold in the U.S. Although tariffs are levied separately from taxes, economists say that much of their impact would be passed along to consumers, making them analogous to a tax.

The video’s figure about how much it will cost families is higher than current estimates.

The American Action Forum, a center-right think tank, has projected additional costs per household of $1,700 to $2,350 annually.

The Peterson Institute of International Economics, another Washington, D.C.-based think tank, projected that such tariffs would cost a middle-income household about $1,700 extra each year.

PolitiFact Chief Correspondent Louis Jacobson, Senior Correspondent Amy Sherman, Staff Writers Jeff Cercone, Samantha Putterman, Sara Swann, Loreben Tuquero and Maria Ramirez Uribe contributed to this story.

Our convention fact-checks rely on both new and previously reported work. We link to past work whenever possible. In some cases, a fact-check rating may be different tonight than in past versions. In those cases, either details of what the candidate said, or how the candidate said it, differed enough that we evaluated it anew.

Our Sources

Please see sources linked in story.

Browse the Truth-O-Meter

More by politifact staff.

IMAGES

How To Write A Statistics Assignment?
Statistics Assignment Examples : Introduction
PPT
Statistics Assignment Examples : Introduction
Statistics Assignment Examples
Statistics Assignment Examples : Introduction

COMMENTS

Statistics Definition (Types, Importance and Examples)
Statistics Definition: Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process in order to effectively produce the results. In short, statistics is a crucial process which helps to make the decision ...
Statistics Definitions, Types, Formulas & Applications
Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics. However, there are two important and basic ideas involved in statistics; they are ...
Ch. 1 Introduction
There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a television news program, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best ...
Statistics
Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, [8] or as a branch of mathematics. [9] Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is generally concerned with the use of data in ...
The Beginner's Guide to Statistical Analysis
Table of contents. Step 1: Write your hypotheses and plan your research design. Step 2: Collect data from a sample. Step 3: Summarize your data with descriptive statistics. Step 4: Test hypotheses or make estimates with inferential statistics.
1.4: Definitions of Statistics, Probability, and Key Terms
Key Terms. In statistics, we generally want to study a population.You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a sample.The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population.
AP®︎ Statistics
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
Introduction to Statistics
Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. ... The text dose lend itself to reasonable reading assignments. For example the chapter (Chapter 3 ...
Khan Academy
Khanmigo is now free for all US educators! Plan lessons, develop exit tickets, and so much more with our AI teaching assistant.
1: Introduction to Statistics
Statistics is a study of data: describing properties of data (descriptive statistics) and drawing conclusions about a population based on information in a sample (inferential statistics). The distinction between a population together with its parameters and a sample together with its statistics is a fundamental concept in inferential statistics ...
PDF Introduction to Statistics
Statistics is a branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations. We begin by introducing two general types of statistics: •• Descriptive statistics: statistics that summarize observations. •• Inferential statistics: statistics used to interpret the meaning of descriptive statistics.
PDF Module 1: Introduction to Statistics
The Role of Statistics ! Despite the anxiety usually associated with statistics, data analysis is a relatively small piece of the larger research process. ! There is a misconception that the trustworthiness of statistics is independent of the research process itself. ! This is absolutely incorrect! !
What Is Statistics? Importance, Scope, Limitations
Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data. Statistics is a set of decision-making techniques which helps businessmen in making suitable policies from the available data. In fact, every businessman needs a sound background of statistics as well as of mathematics.
Statistics: Definition, Types, and Importance
Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies ...
Descriptive Statistics
Types of descriptive statistics. There are 3 main types of descriptive statistics: The distribution concerns the frequency of each value. The central tendency concerns the averages of the values. The variability or dispersion concerns how spread out the values are. You can apply these to assess only one variable at a time, in univariate ...
Descriptive Statistics
Types of descriptive statistics. There are 3 main types of descriptive statistics: The distribution concerns the frequency of each value. The central tendency concerns the averages of the values. The variability or dispersion concerns how spread out the values are. You can apply these to assess only one variable at a time, in univariate ...
Random Sampling vs. Random Assignment
Random assignment is a fundamental part of a "true" experiment because it helps ensure that any differences found between the groups are attributable to the treatment, rather than a confounding variable. So, to summarize, random sampling refers to how you select individuals from the population to participate in your study.
Random Selection vs. Random Assignment
Random selection and random assignment are two techniques in statistics that are commonly used, but are commonly confused.. Random selection refers to the process of randomly selecting individuals from a population to be involved in a study.. Random assignment refers to the process of randomly assigning the individuals in a study to either a treatment group or a control group.
Inferential Statistics
Example: Inferential statistics. You randomly select a sample of 11th graders in your state and collect data on their SAT scores and other characteristics. You can use inferential statistics to make estimates and test hypotheses about the whole population of 11th graders in the state based on your sample data.
Probability and Statistics
Whereas statistics is more about how we handle various data using different techniques. It helps to represent complicated data in a very easy and understandable way. Statistics and probability are usually introduced in Class 10, Class 11 and Class 12 students are preparing for school exams and competitive examinations.
Ch. 1 Key Terms
Introduction; 9.1 Null and Alternative Hypotheses; 9.2 Outcomes and the Type I and Type II Errors; 9.3 Distribution Needed for Hypothesis Testing; 9.4 Rare Events, the Sample, and the Decision and Conclusion; 9.5 Additional Information and Full Hypothesis Test Examples; 9.6 Hypothesis Testing of a Single Mean and Single Proportion; Key Terms; Chapter Review; Formula Review
Assignments
Assignments. The assignments for Concepts in Statistics are typically centered around a dataset that the student uses in conjunction with a statistics package. The activity has the student explore the dataset, generate descriptive statistics and appropriate graphs from the data, and interpret the output. Instructions are provided for five ...
Khan Academy
Khan Academy
Products
This report presents highlights from 2023 final birth data on key demographic and maternal and infant health indicators. The number of births, the general fertility rate (births per 1,000 females ages 15-44), teen birth rates, the distribution of births by trimester prenatal care began, and the distribution of births by gestational age (less than 37 weeks, 37-38 weeks, 39-40 weeks, and ...
Scottish VAT Assignment Experimental Statistics 2022
This release of experimental statistics on Scottish VAT assignment will include the 2022 estimate and further historical estimates in the back series. The VAT assignment model calculates the ...
Fact-checking DNC Night 2: What speakers got right, wrong
That will define the prices to be paid for prescriptions starting in 2026. For 2027 and 2028, 15 more drugs per year will be chosen for price negotiations. Starting in 2029, 20 more will be chosen ...

Introduction to Statistics

Formats Available

Table of Contents

Ancillary Material

About the Book

About the Contributors

Contribute to this Page

What is Statistics? Importance, Scope, Limitations

What is Statistics?

Statistics Meaning

Statistics Definition

Uses of Statistics in Business Decision Making

Uses of Mathematics for Decision Making

Uses of Statistics in Economics

Functions of Statistics

Condensation

Importance of Statistics

Importance of Statistics in Business and Industry

Scope of Statistics

Presents facts in numerical figures

Limitations of Statistics

Statistics Suits to the Study of Quantitative Data Only

You Might Also Like

Leave a Reply Cancel reply

World's Best Online Courses at One Place

Digital Marketing

Personal Growth

Development

What Is Statistics?

Mean, Median, and Mode

Uses of Statistics

Statistics: Definition, Types, and Importance

Key Takeaways

Descriptive and Inferential Statistics

Descriptive Statistics

Inferential Statistics

Statistical Levels of Measurement

Nominal-level Measurement

Ordinal-level Measurement

Interval-level Measurement

Ratio-level Measurement

Statistics Sampling Techniques

Simple Random Sampling

Systemic Sampling

Stratified Sampling

Cluster Sampling

Why Is Statistics Important?

What’s the Difference Between Descriptive and Inferential Statistics?

Who Uses Statistics?

How Are Statistics Used in Economics and Finance?

Have a thesis expert improve your writing

Descriptive Statistics | Definitions, Types, Examples

Table of contents

Standard deviation

Contingency table

Scatter plots

Cite this Scribbr article

Is this article helpful?

Pritha Bhandari

Random Sampling vs. Random Assignment

Discover How We Assist to Edit Your Dissertation Chapters

Have a language expert improve your writing

Inferential Statistics | An Easy Introduction & Examples

Table of contents

Inferential statistics

Sampling error in inferential statistics

Prevent plagiarism. Run a free check.

Confidence intervals

Comparison tests

Correlation tests

Regression tests

Receive feedback on language, structure, and formatting

Cite this Scribbr article

Is this article helpful?

Pritha Bhandari

Probability And Statistics

Solved Examples

What is Statistics?

Terms Used in Probability and Statistics

Random Experiment