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Graphical Representation of Data

Graphical Representation of Data: Graphical Representation of Data,” where numbers and facts become lively pictures and colorful diagrams . Instead of staring at boring lists of numbers, we use fun charts, cool graphs, and interesting visuals to understand information better. In this exciting concept of data visualization, we’ll learn about different kinds of graphs, charts, and pictures that help us see patterns and stories hidden in data.

There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics .

The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, Astro statistics, and so on . In this article, we have provided everything about the graphical representation of data, including its types, rules, advantages, etc.

Table of Content

What is Graphical Representation

Types of graphical representations, line graphs, histograms , stem and leaf plot , box and whisker plot .

• Graphical Representations used in Maths

Value-Based or Time Series Graphs 

Frequency based, principles of graphical representations, advantages and disadvantages of using graphical system, general rules for graphical representation of data, frequency polygon, solved examples on graphical representation of data.

Graphics Representation is a way of representing any data in picturized form . It helps a reader to understand the large set of data very easily as it gives us various data patterns in visualized form.

There are two ways of representing data,

• Pictorial Representation through graphs.

They say, “A picture is worth a thousand words”.  It’s always better to represent data in a graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in the form of visuals as Human beings process data better in visual form than any other form.

Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time.

Check: Graph and its representations

Comparison between different items is best shown with graphs, it becomes easier to compare the crux of the data about different items. Let’s look at all the different types of graphical representations briefly: 

A line graph is used to show how the value of a particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data and predicting further trends. 

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars. 

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range. 

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point.  

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4).  

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data. 

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole. 

Graphical Representations used in Math’s

Graphs in Math are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths: 

• Value-Based or Time Series Graphs

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values. 

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study.

Also read: Types of Statistical Data

• All types of graphical representations follow algebraic principles.
• When plotting a graph, there’s an origin and two axes.
• The x-axis is horizontal, and the y-axis is vertical.
• The axes divide the plane into four quadrants.
• The origin is where the axes intersect.
• Positive x-values are to the right of the origin; negative x-values are to the left.
• Positive y-values are above the x-axis; negative y-values are below.

• It gives us a summary of the data which is easier to look at and analyze.
• It saves time.
• We can compare and study more than one variable at a time.

Disadvantages

• It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data. 
• Interpretation of graphs can vary based on individual perspectives, leading to subjective conclusions.
• Poorly constructed or misleading visuals can distort data interpretation and lead to incorrect conclusions.

Check : Diagrammatic and Graphic Presentation of Data

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs: 

• Whenever possible, the data source must be mentioned for the viewer.
• Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
• The measurement Unit should be mentioned in the top right corner of the graph.
• The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
• Last but not the least, a suitable title should be chosen.

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval. 

Question 1: What are different types of frequency-based plots? 

Types of frequency-based plots:  Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels. 

Draw a bar graph for the following data. 

• Put each of the channels on the x-axis
• The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following data 

• Put each of the x-axis row value on the x-axis
• joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data: 

• Draw the class intervals on the x-axis and frequencies on the y-axis.
• Calculate the midpoint of each class interval.

Now join the mid points of the intervals and their corresponding frequencies on the graph. 

This graph shows both the histogram and frequency polygon for the given distribution.

Related Article:

Graphical Representation of Data| Practical Work in Geography Class 12 What are the different ways of Data Representation What are the different ways of Data Representation? Charts and Graphs for Data Visualization

Conclusion of Graphical Representation

Graphical representation is a powerful tool for understanding data, but it’s essential to be aware of its limitations. While graphs and charts can make information easier to grasp, they can also be subjective, complex, and potentially misleading . By using graphical representations wisely and critically, we can extract valuable insights from data, empowering us to make informed decisions with confidence.

Graphical Representation of Data – FAQs

What are the advantages of using graphs to represent data.

Graphs offer visualization, clarity, and easy comparison of data, aiding in outlier identification and predictive analysis.

What are the common types of graphs used for data representation?

Common graph types include bar, line, pie, histogram, and scatter plots , each suited for different data representations and analysis purposes.

How do you choose the most appropriate type of graph for your data?

Select a graph type based on data type, analysis objective, and audience familiarity to effectively convey information and insights.

How do you create effective labels and titles for graphs?

Use descriptive titles, clear axis labels with units, and legends to ensure the graph communicates information clearly and concisely.

How do you interpret graphs to extract meaningful insights from data?

Interpret graphs by examining trends, identifying outliers, comparing data across categories, and considering the broader context to draw meaningful insights and conclusions.

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Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

MCQ on Graphical Representation of Data

Graphical representation of data uses charts, graphs, and diagrams to visually present information and patterns. It enhances understanding, aids in data analysis, and simplifies complex data, making it accessible to a wider audience. Explore our interactive quiz or MCQ on Graphical Representation of Data to test your comprehension of various graphs, charts, and their applications.

You may also like : Graphical Representation of Data Notes | PPT on Graphical Representation of Data |

You may also like: Biostatistics Notes   |   Biostatistics PPT   |   Biostatistics MCQs   |

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Representing data

Here you will learn about representing data, including how to create and interpret the different tables, charts, diagrams and graphs you can use to represent data.

Students first learn how to represent and interpret data in the first grade and expand their knowledge as they progress through elementary school, middle school and high school. Being data literate is essential for success in the real world.

What is representing data?

Representing data allows you to display and interpret collected data. Data literacy is essential to understanding the world around us.

There are different types of data that can be represented in different formats.

For example,

Stem and leaf plot

• Frequency distribution (such as bar graphs, vertical line graphs & line plots)

Cumulative frequency

Let’s take a look in detail at some of the different ways to represent data.

[FREE] Representing Data Worksheet (Grade 6 to 7)

Use this quiz to check your grade 6th to 7th students’ understanding of representing data. 10+ questions with answers covering a range of grades 6 and 7 representing data topics to identify areas of strength and support!

A histogram is a graphical representation used to display quantitative continuous data (numeric data). The graphical display uses bars that are different heights and each bar groups numbers into ranges. The horizontal axis represents the numerical range, and the vertical axis represents the frequency, which is the number of times the data falls in the particular numerical range.

For example, the frequency table shows the salaries of 157 employees at a small company. Create a histogram from the data.

Step by step guide : Histograms

A stem and leaf plot is a method of organizing numerical data based on the place value of the numbers.

Each number is split into two parts.

The first digit(s) form the stem,

The last digit forms the leaf.

For example, the data below represents the age of all the employees at Millstown Elementary School. Create a stem and leaf plot from the data

Step by step guide: Stem and Leaf Plot

Frequency distribution

A frequency distribution is a way of representing data from a frequency distribution table. Frequency distributions can be represented by frequency graphs such as pie graphs, bar graphs, line plots, vertical line graphs, and/or frequency polygons where the frequency is displayed on the vertical axis (y- axis ).

There are two types of data that can be represented using a frequency graph.

Categorical data – data that are words rather than numbers, for example, colors, makes of cars, types of music.

Numerical data – data that is in the form of numbers. There are two types of numerical data.

Here are some examples of frequency graphs:

Step by step guide: Frequency distribution

Step by step guide: Line graph

A cumulative frequency graph, also called an ogive, shows the frequencies of each category accumulated together. This allows you to analyze the distribution of the data in more detail than if you used a frequency polygon and calculate statistics.

Here is an example of a cumulative frequency graph along with the data set.

Similar to a frequency graph, the horizontal axis (x- axis ) represents the numerical interval and the vertical axis (y- axis ) represents the cumulative frequency.

A pie chart also known as a circle chart or pie graph is a visual representation of data that is made by a circle divided into sectors (pie slices). Each sector represents a part of the whole (whole pie). Pie charts are used to represent categorical data.

Here is an example of a pie chart that displays students’ favorite subjects in percentages at a particular school. Notice how each sector represents a percent of the whole circle.

The sectors of the circle graphs can be represented as the number data points in the category or as percents.

Step by step guide: Pie chart

A box plot also known as a box and whisker plot is a graph that represents the five number summary of a set of data.

The five number summary includes the following:

• Lowest value or smallest value
• Lower quartile or first quartile (Q1)
• Median , middle number , middle value , or second quartile (M)
• Upper quartile or third quartile (Q3)
• Highest value or largest value

Here is an example of a box plot for the given data set:

7, \, 4, \, 5, \, 6, \, 3, \, 4, \, 7, \, 10, \, 11, \, 8, \, 9, \, 2, \, 3, \, 8, \, 11, \, 12, \, 10

Like with a stem and leaf plot, it is helpful to put the data points in order from least to greatest.

2, \, 3, \, 3, \, 4, \, 4, \, 5, \, 6, \, 7, \, 7, \, 8, \, 8, \, 9, \, 10, \, 10, \, 11, \, 11, \, 12

Quartiles are values that divide the data set into three quarters. From the box plot, you can see that the first quartile is the value where the 25\% of the data set falls under.

The median or the second quartile is the value where 50\% of the data falls under and the third quartile (Q3) is the value where 75\% of the data set falls under.

From the box plot, you can also determine the interquartile range (IQR) which is found by finding the difference between Q1 and Q3.

Step by step guide: Box plot

Step by step guide: Quartile

Step by step guide: Interquartile range

Common Core State Standards

How does this relate to 6 th and 7 th grade math?

• Grade 6 – Statistics and Probability (6.SP.B.4) Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
• Grade 6 – Statistics and Probability (6.SP.A.3) Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
• Grade 6 – Ratios and Proportional Relationships (6.RP.3.c) Find a percent of a quantity as a rate per 100 (for example, 30\% of a quantity means \cfrac{30}{100} times the quantity); solve problems involving finding the whole, given a part and the percent.
• Grade 7 – Statistics and Probability (7.SP.B.3) Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10~{cm} greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
• Grade 7 – Statistics and Probability (7.SP.B.4) Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

How to represent data

For a more detailed step-by-step approach on how to represent data, go to the links highlighted in the “What is representing data” section above or follow the examples below.

Representing data examples

Example 1: stem and leaf diagram.

The data below represents the heights of trees at a tree farm in feet.

20ft, \, 15ft, \, 17ft, \, 29ft, \, 22ft, \, 13ft, \, 30ft, \, 25ft, \, 18ft, \, 27ft, \, 31ft

• Order the numbers from smallest to largest.

13, \, 15, \, 17, \, 18, \, 20, \, 22, \, 25, \, 27, \, 29, \, 30, \, 31

2 Split the numbers into two parts; the last part must be one digit only.

The numbers in the data will be split into tens and ones, so 13 will be 1 and 3 (1 represents 10 or 1 ten and 3 is 3 ones ).

3 Put the values into the diagram and create a key.

Example 2: histogram

Create histogram for the given test scores.

\begin{aligned} &82, \, 78, \, 77, \, 89, \, 90, \, 99, \, 97, \, 65, \, 66, \, 74, \, 78, \, 80, \, 78, \\ &92, \, 70, \, 85, \, 75, \, 85, \, 88, \, 79, \, 69, \, 88, \, 99, \, 84, \, 83, \, 91 \end{aligned}

Decide what bin size to use and how many bins are needed.

Bin size is the same as interval size.

The lowest test score is 65 , and the highest test score is 100. Let’s use bins (intervals) of 5. There are 7 bins all together.

Group the data by the bin sizes to find the frequency.

Create bars based on the bin sizes and frequencies within the bins.

Label the \textbf{x} and \textbf{y} axes with units.

Example 3: pie chart

24 pupils were asked which subject was their favorite. Here is a pie chart to show the results. How many students said science was their favorite subject?

Identify the categories.

There are 5 categories, science 25\%, English 13\%, history 20\%, art 10\%, and other 32\%.

Calculate and analyze the data.

There are 24 students that were surveyed, and 25\% said that science was their favorite subject.

24 \times 0.25=6

6 students say that science is their favorite subject.

Example 4: box plot

Create a box plot for the data below.

15, \, 11, \, 24, \, 13, \, 22, \, 17, \, 20, \, 25, \, 19, \, 10, \, 24

Determine the median and quartiles.

Placing the data in order from least to greatest.

10, \, 11, \, 13, \, 15, \, 17, \, 19, \, 20, \, 22, \, 24, \, 24, \, 25

Draw a scale, and mark the five key values: minimum value, lower quartile (LQ), median, upper quartile (UQ), and maximum value.

Join the lower quartile and upper quartile to form the box, and draw horizontal lines to the minimum and maximum values.

Example 5: frequency distribution

At the local zoo, the zoologist was taking a count of the animals.

Create a dot plot representing this data.

Read the question and determine what type of graph you need to create.

This question asks you to create a dot plot to represent the data.

Use the data to create the specific frequency graph.

Example 6: frequency polygon

A vet weighs all the dogs she sees in a week. Here are the results.

Draw a frequency polygon to show the results.

This question asks you to create a frequency polygon to represent the data.

Use the midpoints of the groups representing mass, 5, \, 15, \, 25 and so on, to label the horizontal axis. The frequency is on the vertical axis.

Plot points with a sharp pencil and crosses to be accurate, and then connect the points to create the frequency polygon.

Teaching tips for representing data

• Utilize interactive programs like Excel to allow students to spend time exploring how changing the bin size for a set of data affects the distribution of the data, therefore affecting the conclusions that might be drawn.
• Use project based learning activities where students can collect their own raw data and create and interpret tables, diagrams, and graphs.
• Provide visual aids or display examples of data representation around the classroom for students to differentiate between graph types including stem and leaf plots, bar graphs, histograms, dot plots, and box plots.

Easy mistakes to make

• Knowing when to label the horizontal axis as discrete groups or having it be a continuous scale The horizontal axis of a bar chart is divided into discrete categorical variables with gaps between the bars. Whereas on a histogram, values are on a continuous scale, so there are no gaps between the bins.
• Forgetting to order the data set before creating graphs If you are given a data set to represent on a box plot, stem and leaf plot, histogram, line plots, and/or bar graphs, make sure the list of values is in order before you start finding the key values. Listing the data in order is always a good practice to use when graphing and analyzing data.
• Not being precise when labeling axes When drawing graphs, diagrams, and charts, use a sharp pencil and a ruler so that you can be as accurate as possible. For pie charts, use a protractor to measure the angles accurately.

Practice representing data questions

1. Use the stem and leaf plot to determine the mode.

The value 157~{cm} occurs twice. Therefore, the mode is 157.

2. Use the box plot to determine the median.

On a box plot, the line in the box represents the median.

3. Which histogram represents the data?

The table shows the number of deer Karen sees in her yard over the course of a month.

Look to make sure the axes are numbered correctly. The horizontal axis should be labeled 0 to 20 counting by 5’ s. The vertical axis should be numbered 0 to 10.

Each bar height should be equal to the frequency in each interval.

4. Which pie chart represents the data in this frequency table?

The total of the frequencies is 40. The frequency of A is 10, which is a quarter of 40. So, section A needs to be a quarter of the pie chart.

Similarly section C needs to be a quarter too. The frequency of B is 20, which is half of 40. Section B needs to be half of the pie chart.

5. The table below shows the number of flowers in a garden.

Which dot plot represents the data in the table?

There are 4   types of flowers: tulip, lily, rose, and marigold. Label the horizontal axes with the flower types. For each flower, place the number of dots vertically that matches the frequency.

6. Which of these is the correct frequency polygon for the frequency table below?

The points should be plotted using the midpoints of the groups: 10, \, 30, \, 50, \, 70 and 90. They should be plotted using the correct frequencies: 1, \, 9, \, 8, \, 3 and 2. The points need joining up, but NOT the last and the first points.

Representing data FAQs

Continuous data can be any value within a range of values or in an interval. Discrete data is a specific value within a range.

When you study algebra 1, you will learn how to create scatter plots. A straight line going through the points on a scatter plot is known as a line of best fit. Step-by-step guide: Scatterplots

The next lessons are

• Frequency table
• Frequency graph
• Sampling methods
• Two way tables

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Module 11: Statistics: Describing Data

Representing data graphically, learning outcomes.

• Create a frequency table, bar graph, pareto chart, pictogram, or a pie chart to represent a data set
• Identify features of ineffective representations of data
• Create a histogram, pie chart, or frequency polygon that represents numerical data
• Create a graph that compares two quantities

In this lesson we will present some of the most common ways data is represented graphically.  W e will also discuss some of the ways you can increase the accuracy and effectiveness of graphs of data that you create.

Presenting Categorical Data Graphically

Visualizing data.

Categorical, or qualitative, data are pieces of information that allow us to classify the objects under investigation into various categories. We usually begin working with categorical data by summarizing the data into a frequency table.

Frequency Table

A frequency table is a table with two columns. One column lists the categories, and another for the frequencies with which the items in the categories occur (how many items fit into each category).

An insurance company determines vehicle insurance premiums based on known risk factors. If a person is considered a higher risk, their premiums will be higher. One potential factor is the color of your car. The insurance company believes that people with some color cars are more likely to get in accidents. To research this, they examine police reports for recent total-loss collisions. The data is summarized in the frequency table below.

Sometimes we need an even more intuitive way of displaying data. This is where charts and graphs come in.  There are many, many ways of displaying data graphically, but we will concentrate on one very useful type of graph called a bar graph.  In this section we will work with bar graphs that display categorical data; the next section will be devoted to bar graphs that display quantitative data.

A bar graph is a graph that displays a bar for each category with the length of each bar indicating the frequency of that category.

To construct a bar graph, we need to draw a vertical axis and a horizontal axis.  The vertical direction will have a scale and measure the frequency of each category; the horizontal axis has no scale in this instance.  The construction of a bar chart is most easily described by use of an example.

Using our car data from above, note the highest frequency is 52, so our vertical axis needs to go from 0 to 52, but we might as well use 0 to 55, so that we can put a hash mark every 5 units:

Notice that the height of each bar is determined by the frequency of the corresponding color.  The horizontal gridlines are a nice touch, but not necessary.  In practice, you will find it useful to draw bar graphs using graph paper, so the gridlines will already be in place, or using technology.  Instead of gridlines, we might also list the frequencies at the top of each bar, like this:

The following video explains the process and value of moving data from a table to a bar graph.

In this case, our chart might benefit from being reordered from largest to smallest frequency values. This arrangement can make it easier to compare similar values in the chart, even without gridlines. When we arrange the categories in decreasing frequency order like this, it is called a Pareto chart .

Pareto chart

A Pareto chart is a bar graph ordered from highest to lowest frequency

Transforming our bar graph from earlier into a Pareto chart, we get:

The following video addressed Pareto charts.

In a survey [1] , adults were asked whether they personally worried about a variety of environmental concerns. The numbers (out of 1012 surveyed) who indicated that they worried “a great deal” about some selected concerns are summarized below.

This data could be shown graphically in a bar graph:

To show relative sizes, it is common to use a pie chart.

A pie chart is a circle with wedges cut of varying sizes marked out like slices of pie or pizza.  The relative sizes of the wedges correspond to the relative frequencies of the categories.

For our vehicle color data, a pie chart might look like this:

Pie charts can often benefit from including frequencies or relative frequencies (percents) in the chart next to the pie slices. Often having the category names next to the pie slices also makes the chart clearer.

This video demonstrates how to create pie charts like the ones above.

The pie chart below shows the percentage of voters supporting each candidate running for a local senate seat.

If there are 20,000 voters in the district, the pie chart shows that about 11% of those, about 2,200 voters, support Reeves.

The following video addresses how to read a pie chart like the one above.

Pie charts look nice, but are harder to draw by hand than bar charts since to draw them accurately we would need to compute the angle each wedge cuts out of the circle, then measure the angle with a protractor. Computers are much better suited to drawing pie charts. Common software programs like Microsoft Word or Excel, OpenOffice.org Write or Calc, or Google Drive are able to create bar graphs, pie charts, and other graph types. There are also numerous online tools that can create graphs. [2]

Create a bar graph and a pie chart to illustrate the grades on a history exam below.

A: 12 students, B: 19 students, C: 14 students, D: 4 students, F: 5 students

Here is another way that fanciness can lead to trouble. Instead of plain bars, it is tempting to substitute meaningful images. This type of graph is called a pictogram .

A pictogram is a statistical graphic in which the size of the picture is intended to represent the frequencies or size of the values being represented.

Looking at the picture, it would be reasonable to guess that the manager salaries is 4 times as large as the worker salaries – the area of the bag looks about 4 times as large. However, the manager salaries are in fact only twice as large as worker salaries, which were reflected in the picture by making the manager bag twice as tall.

This video reviews the two examples of ineffective data representation in more detail.

Another distortion in bar charts results from setting the baseline to a value other than zero. The baseline is the bottom of the vertical axis, representing the least number of cases that could have occurred in a category. Normally, this number should be zero.

Compare the two graphs below showing support for same-sex marriage rights from a poll taken in December 2008 [3] . The difference in the vertical scale on the first graph suggests a different story than the true differences in percentages; the second graph makes it look like twice as many people oppose marriage rights as support it.

Presenting Quantitative Data Graphically

Visualizing numbers.

Quantitative, or numerical, data can also be summarized into frequency tables.

A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are:

19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0

These scores could be summarized into a frequency table by grouping like values:

Using the table from the first example, it would be possible to create a standard bar chart from this summary, like we did for categorical data:

A histogram is like a bar graph, but where the horizontal axis is a number line.

For the values above, a histogram would look like:

Notice that in the histogram, a bar represents values on the horizontal axis from that on the left hand-side of the bar up to, but not including, the value on the right hand side of the bar. Some people choose to have bars start at ½ values to avoid this ambiguity.

This video demonstrates the creation of the histogram from this data.

Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.

If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals .

Class Intervals

Class intervals are groupings of the data. In general, we define class intervals so that

• each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
• we have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.

Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Often time we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.

A histogram of this data would look like:

In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.

The following video walks through this example in more detail.

Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.

To see more about why a pie chart isn’t useful in this case, watch the following.

The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.

$140    $160    $160    $165    $180    $220    $235    $240    $250    $260    $280    $285

$285    $285    $290    $300    $300    $305    $310    $310    $315    $315    $320    $320

$330    $340    $345    $350    $355    $360    $360    $380    $395    $420    $460    $460

When collecting data to compare two groups, it is desirable to create a graph that compares quantities.

The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.

One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.

Frequency polygon

An alternative representation is a frequency polygon . A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.

This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.

The following video explains frequency polygon creation for this example.

• Gallup Poll. March 5-8, 2009. http://www.pollingreport.com/enviro.htm ↵
• For example: http://nces.ed.gov/nceskids/createAgraph/ or http://docs.google.com ↵
• CNN/Opinion Research Corporation Poll. Dec 19-21, 2008, from http://www.pollingreport.com/civil.htm ↵
• Learning Objectives and Introduction. Provided by : Lumen Learning. License : CC BY: Attribution
• Revision and Adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
• Math in Society. Authored by : David Lippman. Located at : http://www.opentextbookstore.com/mathinsociety/ . License : CC BY-SA: Attribution-ShareAlike
• Bar graphs for categorical data. Authored by : OCLPhase2's channel. Located at : https://youtu.be/vwxKf_O3ui0 . License : CC BY: Attribution
• Pareto Chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/Tsvru8DPxBE . License : CC BY: Attribution
• Creating a pie chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/__1f8dKh6yo . License : CC BY: Attribution
• Reading a pie chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/mwa8vQnGr3I . License : CC BY: Attribution
• Bad graphical representations of data. Authored by : OCLPhase2's channel. Located at : https://youtu.be/bFwTZNGNLKs . License : CC BY: Attribution
• numbers-education-kindergarten. Authored by : karanja. Located at : https://pixabay.com/en/numbers-education-kindergarten-738068/ . License : CC0: No Rights Reserved
• Creating a histogram. Authored by : OCLPhase2's channel. Located at : https://youtu.be/180FgZ_cTrE . License : CC BY: Attribution
• Defining class intervals for a frequency table or histogram. Authored by : OCLPhase2's channel. Located at : https://youtu.be/JhshitTtdP0 . License : CC BY: Attribution
• When not use a pie chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/FQ8zmZ56-XA . License : CC BY: Attribution
• Frequency polygons. Authored by : OCLPhase2's channel. Located at : https://youtu.be/rxByzA9MFFY . License : CC BY: Attribution

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Suppose the class was polled about their favorite kind of flower.

Which type of graph would you use to show this data?

It is one of the methods of comparing data by using solid bars to represent unique quantities.

It is a circular representation of data, which is divided into slices to illustrate numerical proportion of a whole.

It uses bars to represent frequency of numerical data that have been organized into intervals.

It is a plot used graph in statistics to show cumulative frequencies.

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Identify what kind of graph is being presented.

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17 Data Visualization Techniques All Professionals Should Know

• 17 Sep 2019

There’s a growing demand for business analytics and data expertise in the workforce. But you don’t need to be a professional analyst to benefit from data-related skills.

Becoming skilled at common data visualization techniques can help you reap the rewards of data-driven decision-making , including increased confidence and potential cost savings. Learning how to effectively visualize data could be the first step toward using data analytics and data science to your advantage to add value to your organization.

Several data visualization techniques can help you become more effective in your role. Here are 17 essential data visualization techniques all professionals should know, as well as tips to help you effectively present your data.

Access your free e-book today.

What Is Data Visualization?

Data visualization is the process of creating graphical representations of information. This process helps the presenter communicate data in a way that’s easy for the viewer to interpret and draw conclusions.

There are many different techniques and tools you can leverage to visualize data, so you want to know which ones to use and when. Here are some of the most important data visualization techniques all professionals should know.

Data Visualization Techniques

The type of data visualization technique you leverage will vary based on the type of data you’re working with, in addition to the story you’re telling with your data .

Here are some important data visualization techniques to know:

• Gantt Chart
• Box and Whisker Plot
• Waterfall Chart
• Scatter Plot
• Pictogram Chart
• Highlight Table
• Bullet Graph
• Choropleth Map
• Network Diagram
• Correlation Matrices

1. Pie Chart

Pie charts are one of the most common and basic data visualization techniques, used across a wide range of applications. Pie charts are ideal for illustrating proportions, or part-to-whole comparisons.

Because pie charts are relatively simple and easy to read, they’re best suited for audiences who might be unfamiliar with the information or are only interested in the key takeaways. For viewers who require a more thorough explanation of the data, pie charts fall short in their ability to display complex information.

2. Bar Chart

The classic bar chart , or bar graph, is another common and easy-to-use method of data visualization. In this type of visualization, one axis of the chart shows the categories being compared, and the other, a measured value. The length of the bar indicates how each group measures according to the value.

One drawback is that labeling and clarity can become problematic when there are too many categories included. Like pie charts, they can also be too simple for more complex data sets.

3. Histogram

Unlike bar charts, histograms illustrate the distribution of data over a continuous interval or defined period. These visualizations are helpful in identifying where values are concentrated, as well as where there are gaps or unusual values.

Histograms are especially useful for showing the frequency of a particular occurrence. For instance, if you’d like to show how many clicks your website received each day over the last week, you can use a histogram. From this visualization, you can quickly determine which days your website saw the greatest and fewest number of clicks.

4. Gantt Chart

Gantt charts are particularly common in project management, as they’re useful in illustrating a project timeline or progression of tasks. In this type of chart, tasks to be performed are listed on the vertical axis and time intervals on the horizontal axis. Horizontal bars in the body of the chart represent the duration of each activity.

Utilizing Gantt charts to display timelines can be incredibly helpful, and enable team members to keep track of every aspect of a project. Even if you’re not a project management professional, familiarizing yourself with Gantt charts can help you stay organized.

5. Heat Map

A heat map is a type of visualization used to show differences in data through variations in color. These charts use color to communicate values in a way that makes it easy for the viewer to quickly identify trends. Having a clear legend is necessary in order for a user to successfully read and interpret a heatmap.

There are many possible applications of heat maps. For example, if you want to analyze which time of day a retail store makes the most sales, you can use a heat map that shows the day of the week on the vertical axis and time of day on the horizontal axis. Then, by shading in the matrix with colors that correspond to the number of sales at each time of day, you can identify trends in the data that allow you to determine the exact times your store experiences the most sales.

6. A Box and Whisker Plot

A box and whisker plot , or box plot, provides a visual summary of data through its quartiles. First, a box is drawn from the first quartile to the third of the data set. A line within the box represents the median. “Whiskers,” or lines, are then drawn extending from the box to the minimum (lower extreme) and maximum (upper extreme). Outliers are represented by individual points that are in-line with the whiskers.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted.

7. Waterfall Chart

A waterfall chart is a visual representation that illustrates how a value changes as it’s influenced by different factors, such as time. The main goal of this chart is to show the viewer how a value has grown or declined over a defined period. For example, waterfall charts are popular for showing spending or earnings over time.

8. Area Chart

An area chart , or area graph, is a variation on a basic line graph in which the area underneath the line is shaded to represent the total value of each data point. When several data series must be compared on the same graph, stacked area charts are used.

This method of data visualization is useful for showing changes in one or more quantities over time, as well as showing how each quantity combines to make up the whole. Stacked area charts are effective in showing part-to-whole comparisons.

9. Scatter Plot

Another technique commonly used to display data is a scatter plot . A scatter plot displays data for two variables as represented by points plotted against the horizontal and vertical axis. This type of data visualization is useful in illustrating the relationships that exist between variables and can be used to identify trends or correlations in data.

Scatter plots are most effective for fairly large data sets, since it’s often easier to identify trends when there are more data points present. Additionally, the closer the data points are grouped together, the stronger the correlation or trend tends to be.

10. Pictogram Chart

Pictogram charts , or pictograph charts, are particularly useful for presenting simple data in a more visual and engaging way. These charts use icons to visualize data, with each icon representing a different value or category. For example, data about time might be represented by icons of clocks or watches. Each icon can correspond to either a single unit or a set number of units (for example, each icon represents 100 units).

In addition to making the data more engaging, pictogram charts are helpful in situations where language or cultural differences might be a barrier to the audience’s understanding of the data.

11. Timeline

Timelines are the most effective way to visualize a sequence of events in chronological order. They’re typically linear, with key events outlined along the axis. Timelines are used to communicate time-related information and display historical data.

Timelines allow you to highlight the most important events that occurred, or need to occur in the future, and make it easy for the viewer to identify any patterns appearing within the selected time period. While timelines are often relatively simple linear visualizations, they can be made more visually appealing by adding images, colors, fonts, and decorative shapes.

12. Highlight Table

A highlight table is a more engaging alternative to traditional tables. By highlighting cells in the table with color, you can make it easier for viewers to quickly spot trends and patterns in the data. These visualizations are useful for comparing categorical data.

Depending on the data visualization tool you’re using, you may be able to add conditional formatting rules to the table that automatically color cells that meet specified conditions. For instance, when using a highlight table to visualize a company’s sales data, you may color cells red if the sales data is below the goal, or green if sales were above the goal. Unlike a heat map, the colors in a highlight table are discrete and represent a single meaning or value.

13. Bullet Graph

A bullet graph is a variation of a bar graph that can act as an alternative to dashboard gauges to represent performance data. The main use for a bullet graph is to inform the viewer of how a business is performing in comparison to benchmarks that are in place for key business metrics.

In a bullet graph, the darker horizontal bar in the middle of the chart represents the actual value, while the vertical line represents a comparative value, or target. If the horizontal bar passes the vertical line, the target for that metric has been surpassed. Additionally, the segmented colored sections behind the horizontal bar represent range scores, such as “poor,” “fair,” or “good.”

14. Choropleth Maps

A choropleth map uses color, shading, and other patterns to visualize numerical values across geographic regions. These visualizations use a progression of color (or shading) on a spectrum to distinguish high values from low.

Choropleth maps allow viewers to see how a variable changes from one region to the next. A potential downside to this type of visualization is that the exact numerical values aren’t easily accessible because the colors represent a range of values. Some data visualization tools, however, allow you to add interactivity to your map so the exact values are accessible.

15. Word Cloud

A word cloud , or tag cloud, is a visual representation of text data in which the size of the word is proportional to its frequency. The more often a specific word appears in a dataset, the larger it appears in the visualization. In addition to size, words often appear bolder or follow a specific color scheme depending on their frequency.

Word clouds are often used on websites and blogs to identify significant keywords and compare differences in textual data between two sources. They are also useful when analyzing qualitative datasets, such as the specific words consumers used to describe a product.

16. Network Diagram

Network diagrams are a type of data visualization that represent relationships between qualitative data points. These visualizations are composed of nodes and links, also called edges. Nodes are singular data points that are connected to other nodes through edges, which show the relationship between multiple nodes.

There are many use cases for network diagrams, including depicting social networks, highlighting the relationships between employees at an organization, or visualizing product sales across geographic regions.

17. Correlation Matrix

A correlation matrix is a table that shows correlation coefficients between variables. Each cell represents the relationship between two variables, and a color scale is used to communicate whether the variables are correlated and to what extent.

Correlation matrices are useful to summarize and find patterns in large data sets. In business, a correlation matrix might be used to analyze how different data points about a specific product might be related, such as price, advertising spend, launch date, etc.

Other Data Visualization Options

While the examples listed above are some of the most commonly used techniques, there are many other ways you can visualize data to become a more effective communicator. Some other data visualization options include:

• Bubble clouds
• Circle views
• Dendrograms
• Dot distribution maps
• Open-high-low-close charts
• Polar areas
• Radial trees
• Ring Charts
• Sankey diagram
• Span charts
• Streamgraphs
• Wedge stack graphs
• Violin plots

Tips For Creating Effective Visualizations

Creating effective data visualizations requires more than just knowing how to choose the best technique for your needs. There are several considerations you should take into account to maximize your effectiveness when it comes to presenting data.

Related : What to Keep in Mind When Creating Data Visualizations in Excel

One of the most important steps is to evaluate your audience. For example, if you’re presenting financial data to a team that works in an unrelated department, you’ll want to choose a fairly simple illustration. On the other hand, if you’re presenting financial data to a team of finance experts, it’s likely you can safely include more complex information.

Another helpful tip is to avoid unnecessary distractions. Although visual elements like animation can be a great way to add interest, they can also distract from the key points the illustration is trying to convey and hinder the viewer’s ability to quickly understand the information.

Finally, be mindful of the colors you utilize, as well as your overall design. While it’s important that your graphs or charts are visually appealing, there are more practical reasons you might choose one color palette over another. For instance, using low contrast colors can make it difficult for your audience to discern differences between data points. Using colors that are too bold, however, can make the illustration overwhelming or distracting for the viewer.

Related : Bad Data Visualization: 5 Examples of Misleading Data

Visuals to Interpret and Share Information

No matter your role or title within an organization, data visualization is a skill that’s important for all professionals. Being able to effectively present complex data through easy-to-understand visual representations is invaluable when it comes to communicating information with members both inside and outside your business.

There’s no shortage in how data visualization can be applied in the real world. Data is playing an increasingly important role in the marketplace today, and data literacy is the first step in understanding how analytics can be used in business.

Are you interested in improving your analytical skills? Learn more about Business Analytics , our eight-week online course that can help you use data to generate insights and tackle business decisions.

This post was updated on January 20, 2022. It was originally published on September 17, 2019.

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• RD Sharma Solutions
• Chapter 24 Graphical Representation Of Data As Histograms

RD Sharma Solutions for Class 8 Maths Chapter 24 Data Handling - II (Graphical Representation of Data as Histogram)

In the previous class, we learnt how to draw bar graphs to represent the frequency distribution of ungrouped data. In this chapter, we will learn how to represent a grouped frequency distribution graphically. The most common graphic representation is the histogram. Students can utilise the RD Sharma Solutions for Class 8 for any doubt clearance and can also strengthen their conceptual knowledge. When solutions are practised regularly, students can speed up their problem-solving abilities. The PDF of RD Sharma Solutions Class 8 contains questions from this chapter and can be downloaded easily from the links available below.

Chapter 24 Data Handling – II (Graphical Representation of Data as Histogram) contains one exercise, and the RD Sharma Class 8 Solutions available on this page provide solutions to the questions in this exercise. Now, let us have a look at the concepts discussed in this chapter.

• Graphical method of representing data.
• RD Sharma Solutions for Class 8 Maths Chapter 1 Rational Numbers
• RD Sharma Solutions for Class 8 Maths Chapter 2 Powers
• RD Sharma Solutions for Class 8 Maths Chapter 3 Squares and Square Roots
• RD Sharma Solutions for Class 8 Maths Chapter 4 Cubes and Cube Roots
• RD Sharma Solutions for Class 8 Maths Chapter 5 Playing with Numbers
• RD Sharma Solutions for Class 8 Maths Chapter 6 Algebraic Expressions and Identities
• RD Sharma Solutions for Class 8 Maths Chapter 7 Factorization
• RD Sharma Solutions for Class 8 Maths Chapter 8 Division of Algebraic Expressions
• RD Sharma Solutions for Class 8 Maths Chapter 9 Linear Equations in One Variable
• RD Sharma Solutions for Class 8 Maths Chapter 10 Direct and Inverse Variations
• RD Sharma Solutions for Class 8 Maths Chapter 11 Time and Work
• RD Sharma Solutions for Class 8 Maths Chapter 12 Percentage
• RD Sharma Solutions for Class 8 Maths Chapter 13 Profit, Loss, Discount and Value Added Tax (VAT)
• RD Sharma Solutions for Class 8 Maths Chapter 14 Compound Interest
• RD Sharma Solutions for Class 8 Maths Chapter 15 Understanding Shapes – I (Polygons)
• RD Sharma Solutions for Class 8 Maths Chapter 16 Understanding Shapes – II (Quadrilaterals)
• RD Sharma Solutions for Class 8 Maths Chapter 17 Understanding Shapes – II (Special Types of Quadrilaterals)
• RD Sharma Solutions for Class 8 Maths Chapter 18 Practical Geometry (Constructions)
• RD Sharma Solutions for Class 8 Maths Chapter 19 Visualising Shapes
• RD Sharma Solutions for Class 8 Maths Chapter 20 Mensuration – I (Area of a Trapezium and a Polygon)
• RD Sharma Solutions for Class 8 Maths Chapter 21 Mensuration – II (Volumes and Surface Areas of a Cuboid and a Cube)
• RD Sharma Solutions for Class 8 Maths Chapter 22 Mensuration – III (Surface Area and Volume of a Right Circular Cylinder)
• RD Sharma Solutions for Class 8 Maths Chapter 23 Data Handling – I (Classification and Tabulation of Data)
• RD Sharma Solutions for Class 8 Maths Chapter 24 Data Handling – II (Graphical Representation of Data as Histograms)
• RD Sharma Solutions for Class 8 Maths Chapter 25 Data Handling – III (Pictorial Representation of Data as Pie Charts)
• RD Sharma Solutions for Class 8 Maths Chapter 26 Data Handling – IV (Probability)
• RD Sharma Solutions for Class 8 Maths Chapter 27 Introduction to Graphs

RD Sharma Solutions for Class 8 Maths Chapter 24 Data Handling – II (Graphical Representation of Data as Histogram)

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Access Answers to RD Sharma Class 8 Maths Solutions for Chapter 24 Data Handling – II (Graphical Representation of Data as Histogram)

1. Given below is the frequency distribution of the heights of 50 students in a class:

Draw a histogram representing the above data.

The class limits are represented along the x-axis on a suitable scale, and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain the histogram of the given frequency distribution, as shown in the figure below:

2. Draw a histogram of the following data:

The class limits are represented along the x-axis, and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

3. Number of workshops organised by a school in different areas during the last five years are as follows:

Draw a histogram representing the above data:

The class limits are represented along the x-axis, and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain a histogram for the given frequency. The histogram is shown below:

4. In a hypothetical sample of 20 people, the amounts of money with them were found to be as follows: 114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 168, 182, 195, 207, 219, 235, 118. Draw the histogram of the frequency distribution (taking one of the class intervals as 50-100).

First, prepare the frequency table for the class intervals 50−100, 100−150,…, 200−250, as shown below:

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking the class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

5. Construct a histogram for the following data:

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and corresponding frequencies as heights of the rectangles, the histogram of the given data can be obtained as shown in the figure below:

6. Draw a histogram for the daily earnings of 30 drug stores in the following table:

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is given below:

7. Draw a histogram to represent the following data:

Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain the histogram of the given data. The class intervals are represented along the x-axis and the frequencies along the y-axis on a suitable scale.

The histogram representing the given data is shown below:

(i) The highest rectangle corresponds to the highest number of literate females, which is in the interval of 15−20 years.

(ii) The class intervals are 10−15, 15−20, 20−25, 30−35 and 35−40. Hence, the class width is 5.

(iii) The lowest rectangle corresponds to the lowest frequency, which is 320.

(iv) The class mark is the mid-point of the class interval.

i.e., Class mark = (upper limit + lower limit) / 2

Hence, the class mark of each class is as follows:

(v) The lowest rectangle corresponds to the least number of literate females, which is in the interval of 10−15 years.

(i) From the figure, the highest rectangle corresponds to the largest number of workers. The required interval is Rs. 950−1000. There are 8 workers in this interval.

(ii) The lowest rectangle corresponds to the least number of workers. The required interval is Rs. 900−950. There are 2 workers in this interval.

(iii) The total number of workers is the sum of workers in all the intervals. It can be calculated as follows:

Total workers = 3 + 7 + 5 + 4 + 2 + 8 + 6 + 5 = 40 workers

(iv) The factory intervals are 750−800, 800−850, .. 1050−100. Hence, the factory size is 50.

(i) In the given histogram, the interval with the highest marks is 90−100.

Three students are there in this interval because the height of the rectangle (90−100) is 3 units.

(ii) The class intervals are 10−20, 20−30, …, 90−100. So, the class size is 10.

(i) The eldest (50−55 years) = 1 person

This is because the height of the rectangle with class interval 50−55 as the base is 1 unit.

The youngest (20−25 years) = 2 persons

This is because the height of the rectangle with class interval 20−25 as the base is 2 units.

(ii) The group containing the most number of teachers is 35−40 years. This is because the height of the rectangle with class interval 35−40 as the base is the maximum.

The group containing the least number of teachers is 50−55 years. This is because the height of the rectangle with class interval 50−55 as the base is the minimum.

(iii) Class size = The range between the upper and the lower boundaries of the class.

For example, the size of class 20−25 years is 5.

i.e., Class mark = (upper limit + lower limit)/2

For Class 20-25:

Class mark = (20+25)/2 = 45/2 = 22.5

Similarly, the class marks of the other classes are 27.5, 32.5, 37.5, 42.5, 47.5, and 52.5.

12. The weekly wages (in Rs.) of 30 workers in a factory are given below: 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840 Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions: (i) Which group has the maximum number of workers? (ii) How many workers earn Rs. 850 and more? (iii) How many workers earn less then Rs. 850?

The frequency table with intervals 800−820, 810−820,…890−900 is shown below:

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

(i) The group that has the maximum number of workers is represented as the highest rectangle. It is in the interval 830−840.

(ii) The number of workers who earn Rs. 850 or more can be calculated from the frequency table in the following manner:

1 + 3 + 1 + 1 + 4 = 101 + 3 + 1 + 1 + 4 = 10

(iii) The number of workers who earn less than Rs. 850 can be calculated from the frequency table in the following manner:

3 + 2 + 1 + 9 + 5 = 203 + 2 + 1 + 9 + 5 = 20

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• Graphic Presentation of Data

Apart from diagrams, Graphic presentation is another way of the presentation of data and information. Usually, graphs are used to present time series and frequency distributions. In this article, we will look at the graphic presentation of data and information along with its merits, limitations , and types.

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Construction of a graph.

The graphic presentation of data and information offers a quick and simple way of understanding the features and drawing comparisons. Further, it is an effective analytical tool and a graph can help us in finding the mode, median, etc.

We can locate a point in a plane using two mutually perpendicular lines – the X-axis (the horizontal line) and the Y-axis (the vertical line). Their point of intersection is the Origin .

We can locate the position of a point in terms of its distance from both these axes. For example, if a point P is 3 units away from the Y-axis and 5 units away from the X-axis, then its location is as follows:

Browse more Topics under Descriptive Statistics

• Definition and Characteristics of Statistics
• Stages of Statistical Enquiry
• Importance and Functions of Statistics
• Nature of Statistics – Science or Art?
• Application of Statistics
• Law of Statistics and Distrust of Statistics
• Meaning and Types of Data
• Methods of Collecting Data
• Sample Investigation
• Classification of Data
• Tabulation of Data
• Frequency Distribution of Data
• Diagrammatic Presentation of Data
• Measures of Central Tendency
• Mean Median Mode
• Measures of Dispersion
• Standard Deviation
• Variance Analysis

Some points to remember:

• We measure the distance of the point from the Y-axis along the X-axis. Similarly, we measure the distance of the point from the X-axis along the Y-axis. Therefore, to measure 3 units from the Y-axis, we move 3 units along the X-axis and likewise for the other coordinate .
• We then draw perpendicular lines from these two points.
• The point where the perpendiculars intersect is the position of the point P.
• We denote it as follows (3,5) or (abscissa, ordinate). Together, they are the coordinates of the point P.
• The four parts of the plane are Quadrants.
• Also, we can plot different points for a different pair of values.

General Rules for Graphic Presentation of Data and Information

There are certain guidelines for an attractive and effective graphic presentation of data and information. These are as follows:

• Suitable Title – Ensure that you give a suitable title to the graph which clearly indicates the subject for which you are presenting it.
• Unit of Measurement – Clearly state the unit of measurement below the title.
• Suitable Scale – Choose a suitable scale so that you can represent the entire data in an accurate manner.
• Index – Include a brief index which explains the different colors and shades, lines and designs that you have used in the graph. Also, include a scale of interpretation for better understanding.
• Data Sources – Wherever possible, include the sources of information at the bottom of the graph.
• Keep it Simple – You should construct a graph which even a layman (without any exposure in the areas of statistics or mathematics) can understand.
• Neat – A graph is a visual aid for the presentation of data and information. Therefore, you must keep it neat and attractive. Choose the right size, right lettering, and appropriate lines, colors, dashes, etc.

Merits of a Graph

• The graph presents data in a manner which is easier to understand.
• It allows us to present statistical data in an attractive manner as compared to tables. Users can understand the main features, trends, and fluctuations of the data at a glance.
• A graph saves time.
• It allows the viewer to compare data relating to two different time-periods or regions.
• The viewer does not require prior knowledge of mathematics or statistics to understand a graph.
• We can use a graph to locate the mode, median, and mean values of the data.
• It is useful in forecasting, interpolation, and extrapolation of data.

Limitations of a Graph

• A graph lacks complete accuracy of facts.
• It depicts only a few selected characteristics of the data.
• We cannot use a graph in support of a statement.
• A graph is not a substitute for tables.
• Usually, laymen find it difficult to understand and interpret a graph.
• Typically, a graph shows the unreasonable tendency of the data and the actual values are not clear.

Types of Graphs

Graphs are of two types:

• Time Series graphs
• Frequency Distribution graphs

Time Series Graphs

A time series graph or a “ histogram ” is a graph which depicts the value of a variable over a different point of time. In a time series graph, time is the most important factor and the variable is related to time. It helps in the understanding and analysis of the changes in the variable at a different point of time. Many statisticians and businessmen use these graphs because they are easy to understand and also because they offer complex information in a simple manner.

Further, constructing a time series graph does not require a user with technical skills. Here are some major steps in the construction of a time series graph:

• Represent time on the X-axis and the value of the variable on the Y-axis.
• Start the Y-value with zero and devise a suitable scale which helps you present the whole data in the given space.
• Plot the values of the variable and join different point with a straight line.
• You can plot multiple variables through different lines.

You can use a line graph to summarize how two pieces of information are related and how they vary with each other.

• You can compare multiple continuous data-sets easily
• You can infer the interim data from the graph line

Disadvantages

• It is only used with continuous data.

Use of a false Base Line

Usually, in a graph, the vertical line starts from the Origin. However, in some cases, a false Base Line is used for a better representation of the data. There are two scenarios where you should use a false Base Line:

• To magnify the minor fluctuation in the time series data
• To economize the space

Net Balance Graph

If you have to show the net balance of income and expenditure or revenue and costs or imports and exports, etc., then you must use a net balance graph. You can use different colors or shades for positive and negative differences.

Frequency Distribution Graphs

Let’s look at the different types of frequency distribution graphs.

A histogram is a graph of a grouped frequency distribution. In a histogram, we plot the class intervals on the X-axis and their respective frequencies on the Y-axis. Further, we create a rectangle on each class interval with its height proportional to the frequency density of the class.

Frequency Polygon or Histograph

A frequency polygon or a Histograph is another way of representing a frequency distribution on a graph. You draw a frequency polygon by joining the midpoints of the upper widths of the adjacent rectangles of the histogram with straight lines.

Frequency Curve

When you join the verticals of a polygon using a smooth curve, then the resulting figure is a Frequency Curve. As the number of observations increase, we need to accommodate more classes. Therefore, the width of each class reduces. In such a scenario, the variable tends to become continuous and the frequency polygon starts taking the shape of a frequency curve.

Cumulative Frequency Curve or Ogive

A cumulative frequency curve or Ogive is the graphical representation of a cumulative frequency distribution. Since a cumulative frequency is either of a ‘less than’ or a ‘more than’ type, Ogives are of two types too – ‘less than ogive’ and ‘more than ogive’.

Scatter Diagram

A scatter diagram or a dot chart enables us to find the nature of the relationship between the variables. If the plotted points are scattered a lot, then the relationship between the two variables is lesser.

Solved Question

Q1. What are the general rules for the graphic presentation of data and information?

Answer: The general rules for the graphic presentation of data are:

• Use a suitable title
• Clearly specify the unit of measurement
• Ensure that you choose a suitable scale
• Provide an index specifying the colors, lines, and designs used in the graph
• If possible, provide the sources of information at the bottom of the graph
• Keep the graph simple and neat.

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Descriptive Statistics

• Nature of Statistics – Science or Art?

2 responses to “Stages of Statistical Enquiry”

Im trying to find out if my mother ALICE Desjarlais is registered with the Red Pheasant Reserve, I applied with Metie Urban Housing and I need my Metie card. Is there anyway you can help me.

Quite useful details about statistics. I’d also like to add one point. If you need professional help with a statistics project? Find a professional in minutes!

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