Courses

Courses for Kids

Free study material

Store

Talk to our experts

1800-120-456-456

RS Aggarwal Solutions

RS Aggarwal Class 8 Mathematics Solutions Chapter-21 Data Handling

RS Aggarwal Class 8 Mathematics Solutions Chapter-21 Data Handling

Q: 2. What is the main difference between a bar graph and a histogram when solving problems in Chapter 21, and when should I use each?

The primary difference is that a histogram is used for continuous data organised into class intervals (e.g., mark ranges like 10-20, 20-30), and its bars are adjacent with no gaps. A bar graph, on the other hand, is for discrete, separate categories (e.g., favourite sports), and its bars have equal gaps between them. For Chapter 21 exercises, use a histogram for any grouped frequency distribution and a bar graph for distinct, non-continuous items.

Q: 3. While creating a grouped frequency distribution table for RS Aggarwal exercises, how do I decide the class size and avoid common mistakes?

To determine the class size, first calculate the range of your data (Highest Value - Lowest Value). Then, decide on a suitable number of classes, typically between 5 and 10 for clarity. The class size can be approximated by dividing the range by your chosen number of classes. A common mistake to avoid is the improper placement of upper-limit values. For an interval like '10-20', the data point '20' should be included in the next class interval, '20-30', as per the standard exclusive method.

Class 8 RS Aggarwal Maths Data Handling Solutions - Free PDF Download

The solutions of R.S Aggarwal Class 8 Maths Chapter 21 Data Handling by Vedantu are available to the students. Here, you will find solutions to each problem given in RS Aggarwal Class 8 Maths Chapter 21. Expert mathematics teachers have solved all the problems. Each exercise has been taken care of to make the learning experience of the students effortless. The students can download the PDF containing solutions of RS Aggarwal Class 8 Maths Chapter 21 from here. The solutions are explained in the simplest way possible to understand it thoroughly at one go. Before this, the students need to have a thorough idea about data and what is data handling.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful. You can also download NCERT Solutions Class 8 Maths to help you to revise complete syllabus and score more marks in your examinations.

RS Aggarwal Solutions for Class 8 Maths Chapter 21 - Free PDF Download

We have provided step by step solutions for all exercise questions given in the pdf of Class 8 RS Aggarwal Chapter-21 Data Handling. All the Exercise questions with solutions in Chapter-21 Data Handling are given below:

Exercise (Ex 21A) 21.1

Exercise (Ex 21B) 21.2

Exercise (Ex 21C) 21.3

Data Handling - At A Glance

Data handling is an important chapter of class 8 mathematics as it forms a base for future complex chapters like statistics and probability. It is very essential for class 8 students to study these chapters well. Some of the important concepts discussed in the chapter are:

An unorganized form of data is known as raw data.
We should always organize data systematically in order to draw meaningful inferences from the data.
Frequency refers to the number of times a specific entry appears.
Raw data are grouped together systematically in the form of grouped frequency distribution.
Grouped data are represented using the histogram.
Histograms are a type of bar diagram where the horizontal axis is class intervals and bars represent the frequency of the class interval.
Pie charts can also be used to represent data.
The other name for pie charts is circle graphs.
Those experiments whose outcomes cannot be predicted in advance are known as random experiments.
When each outcome in an experiment has an equal chance of occurring then such outcomes are known as equally likely outcomes.
The probability of an experiment is calculated as the number of outcomes of an event divided by the total number of outcomes of the experiment.
More than one outcome of an experiment makes an event.
Concepts of probability and chances are related to real life.

What is Data?

The information or facts that are gathered with the help of observations and measurements is known as data.

The actual meaning of data can only be explained with the help of suitable examples:-

Suppose your class teacher takes a physics unit test for the whole class. She distributes the result the next day, and you find out that you have got 8/10. Similarly, your best friend got an 8.5/10. Likewise, the entire class got some marks. The marks that you and your classmates got is known as Data.

In mathematics, we deal with quantitative data, i.e. the data that can be expressed as numbers. The marks that you and your classmates got are the example of quantitative data.

Another example of data is:-

Suppose your PT teacher measures the weight of each student in the class. Your weight is 50kgs. Your friend’s weight is 49.5 kgs. Likewise, each student has a particular weight. The value of the weight, such as 50,49.5 and so on, are known as data.

Data is of two types: raw data and grouped data.

Raw Data: When the data is collected it is not arranged in a systematic manner and is presented randomly. Such data is known as raw data.
Grouped Data: When the raw data collected is further classified into groups in a systematic manner then that data is known as grouped data.

What is Data Handling?

Data Handling refers to the systematic organisation of data. It involves collecting, recording, analysing, and presenting data that aids in understanding and drawing inferences from the data collected.

Data is generally collected in an unorganised form. This unorganised form of information is known as raw data. Systematic organization of raw data is done in data handling.

For example:-

Suppose, 15 students are asked about choosing their favourite ice cream flavour from chocolate, strawberry, vanilla and other flavours. The response of the students are as follows:-

Strawberry, vanilla, other flavours, vanilla, chocolate, chocolate, vanilla, strawberry, different flavours, vanilla, strawberry, chocolate, vanilla, other flavours, strawberry.

The above data is in the form of raw data. This data needs an organisation to find out the favour that is liked the most.

Ice Cream flavour	Tally Marks	Number of students
Strawberry	IIII	4
Vanilla	IIII	5
Chocolate	III	3
Other Flavour	III	3

The tally marks of each flavour represent the no. of students that like a particular flavour. It is known as the frequency of the flavour. The above table is known as the frequency distribution table.

What is Frequency?

Frequency can be defined as the number of times an observation occurs during a study. In the above example, strawberry ice cream is liked by three students; hence the frequency of strawberry ice cream is 4. Likewise, the frequency of Vanilla, chocolate and other ice cream is 5, 3, 3, respectively.

When we represent the frequency of the data in the form of a table, then that table is known as the frequency distribution table.

What is Grouped Frequency Distribution?

A grouped frequency distribution is required when the number of data is large. For example, a frequency distribution table of marks obtained by 30 students in a mathematics test has to be made, and they are given in the form of raw data. The total marks of the test are 20.

17, 8, 9, 4, 9, 6, 7, 9, 18, 8, 19, 19, 17, 16, 15, 18, 11, 4, 18, 9, 7, 15, 15, 14, 18, 14, 19, 15, 16, 8

Groups(Marks)	Frequency
0 - 10	12
10- 20	18
Total	30

The groups 0-10 and 10- 20 are called class intervals, and the distribution is known as grouped frequency distribution. In group 0-10, 0 is known as the lower class limit, and 10 is known as the upper-class limit. Similarly, in the next group, 10-20, 10 is known as the lower class limit, and 20 is known as the upper-class limit. A histogram represents a grouped frequency distribution.

The difference between the upper-class limit and the lower class limit gives us the class interval’s width or size. The width of each class interval in the above example is 10.

What is the Class Interval?

Class interval is the range of each group in which the raw data is grouped. For example, 1 -10, 11-20, 21-30 are examples of class intervals.

What are Pictographs?

Representation of data by the use of appropriate pictures is known as a pictograph. Each picture or symbol that is used in data presentation represents a certain value.

What are Bar Graphs and Double Bar Graphs?

Bar graphs are pictorial graphs that represent data in the form of bars that have uniform width but whose height varies on the basis of the value of the respective data.

Simultaneous representation of two sets of data in a bar graph is known as a double bar graph. This type of graph is used for the comparison of the data.

Did you know?

Herman Hollerith (1860 - 1929) was a statistician who invented the tabulating machine that helped in data handling to save a significant amount of time while calculating census.

FAQs on RS Aggarwal Class 8 Mathematics Solutions Chapter-21 Data Handling

1. What is the correct method for constructing a histogram for grouped data as required in RS Aggarwal Class 8 Chapter 21?

To correctly construct a histogram for the problems in RS Aggarwal Chapter 21, you must follow these steps precisely:

First, represent the class intervals on the horizontal axis (x-axis) and the corresponding frequencies on the vertical axis (y-axis).
Draw rectangular bars where the width represents the class size and the height corresponds to the frequency of that class.
Crucially, ensure there are no gaps between consecutive bars, as histograms are used to represent continuous data.

2. What is the main difference between a bar graph and a histogram when solving problems in Chapter 21, and when should I use each?

The primary difference is that a histogram is used for continuous data organised into class intervals (e.g., mark ranges like 10-20, 20-30), and its bars are adjacent with no gaps. A bar graph, on the other hand, is for discrete, separate categories (e.g., favourite sports), and its bars have equal gaps between them. For Chapter 21 exercises, use a histogram for any grouped frequency distribution and a bar graph for distinct, non-continuous items.

3. While creating a grouped frequency distribution table for RS Aggarwal exercises, how do I decide the class size and avoid common mistakes?

To determine the class size, first calculate the range of your data (Highest Value - Lowest Value). Then, decide on a suitable number of classes, typically between 5 and 10 for clarity. The class size can be approximated by dividing the range by your chosen number of classes. A common mistake to avoid is the improper placement of upper-limit values. For an interval like '10-20', the data point '20' should be included in the next class interval, '20-30', as per the standard exclusive method.

4. How do the solutions for the different exercises in RS Aggarwal Class 8 Chapter 21 build on each other?

The exercises in RS Aggarwal's Chapter 21 on Data Handling are structured progressively. The initial exercises focus on organising raw data and creating basic frequency distribution tables. Later exercises build on this foundation by requiring you to:

Create grouped frequency tables from larger, more complex datasets.
Use these tables to construct and interpret histograms accurately.
Analyse information presented in existing histograms to answer questions.

Mastering the initial table-creation exercises is essential for success in the later graphical representation problems.

5. Why is it necessary to group data into class intervals instead of plotting each individual data point?

Grouping data into class intervals is essential when dealing with a large dataset. This method summarises the data, making it easier to understand and analyse. If you were to plot every individual data point for a large group, like the heights of 100 students, the graph would be cluttered and would not reveal any clear pattern. By grouping the heights into intervals (e.g., 140-145 cm, 145-150 cm), you can create a histogram that clearly shows the data's distribution and trends.

6. What are the key topics for which step-by-step solutions are provided in RS Aggarwal Class 8 Maths Chapter 21?

The solutions for RS Aggarwal Class 8 Chapter 21 (Data Handling) provide detailed, step-by-step methods for solving problems related to key concepts as per the 2025-26 syllabus. These include:

Arranging raw data and calculating the range.
Constructing frequency distribution tables for both ungrouped and grouped data.
Correctly identifying class marks, class limits, and class size.
Drawing and interpreting histograms for continuous data distributions.

7. When constructing a histogram, what does the 'kink' or 'jagged line' on the x-axis signify?

A 'kink' or 'jagged line' on the horizontal (x-axis) of a histogram indicates a break in the scale. It is used when the class intervals do not start from zero, but from a higher value. For example, if your data for student weights starts from 35 kg, you can use a kink to show that the scale from 0 to 35 has been omitted. This allows the graph to focus on the relevant data range without having a long, empty space on the axis, making the histogram easier to read.