CBSE Class 8 Maths Exemplar Chapter 2: Data Handling NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 8 PDF

CBSE Class 8 Maths Exemplar, Chapter 2: Data Handling, introduces students to the essential techniques for organizing, interpreting, and presenting data. This chapter explores visual representations like histograms, where the height of each rectangle corresponds to the frequency of data within a specific interval, and pie charts, which effectively illustrate proportions of a whole. Students will learn to calculate the range of a dataset, providing a measure of its spread. Furthermore, the concept of probability is explored through practical examples, such as determining the likelihood of selecting a vowel from the English alphabet. The solutions offer clear, step-by-step guidance to help students understand these concepts thoroughly and build a strong foundation in data analysis, crucial for academic success.

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Quick info

Board	CBSE
Class	Class 8
Subject	Maths Exemplar
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 2

Chapter summary

Chapter 2 of the CBSE Class 8 Maths Exemplar focuses on Data Handling. This section provides NCERT Solutions that explain the graphical representation of data, including histograms and pie charts. It covers how to calculate the range of a dataset and introduces the basic concepts of probability with practical examples. The exercises are designed to reinforce understanding of data interpretation and representation techniques.

Learning outcomes

Understand the components of a histogram and their significance.
Identify and explain the use of pie charts for data representation.
Calculate the range of a given set of data.
Define and identify random experiments.
Calculate the probability of simple events.

Topics covered

Paper topics

Histograms
Pie Charts
Data Representation
Range of Data
Random Experiments
Probability

Important topics

Understanding Histograms
Interpreting Pie Charts
Calculating Range
Concept of Probability
Identifying Random Experiments

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Questions and Solutions

Question 1

The height of a rectangle in a histogram shows the

Width of the class
Upper limit of the class
Lower limit of the class
Frequency of the class

Solution: The height of a rectangle in a histogram is a graphical representation that directly indicates the frequency of the data points falling within that particular class interval. Therefore, the correct option is the frequency of the class.

Answer: (d) Frequency of the class

Question 2

A geometric representation showing the relationship between a whole and its parts is a

Pie chart
Histogram
Bar graph
Pictograph

Solution: A pie chart is a circular statistical graphic, divided into slices to illustrate numerical proportion. Each slice's arc length (and consequently its central angle and area) is proportional to the quantity it represents. This makes it ideal for showing how a whole is divided into parts.

Answer: (a) Pie chart

Question 3

In a pie chart, the total angle at the centre of the circle is

$180^{\circ}$
$360^{\circ}$
$270^{\circ}$
$90^{\circ}$

Solution: A pie chart represents a whole, which is depicted as a complete circle. The total angle at the center of any circle is always

360^{\circ}

. This total angle is divided proportionally among the different categories represented in the pie chart.

Answer: (b) $360^{\circ}$

Question 4

The range of the data 30, 61, 55, 56, 60, 20, 26, 46, 28, 56 is

Solution: The range of a data set is the difference between the highest and the lowest observation. First, identify the highest and lowest values in the given data set: {30, 61, 55, 56, 60, 20, 26, 46, 28, 56}. The highest observation is 61, and the lowest observation is 20.

Range = Highest observation - Lowest observation

$Range = 61 - 20$

$Range = 41$

Answer: (c) 41

Question 5

Which of the following is not a random experiment?

Tossing a coin
Rolling a dice
Choosing a card from a deck of 52 cards
Throwing a stone from a roof of a building

Solution: A random experiment is an experiment whose outcome cannot be predicted with certainty, although all possible outcomes are known. Tossing a coin, rolling a die, and choosing a card from a deck are all random experiments because their outcomes are uncertain. However, throwing a stone from a roof has a predictable outcome: the stone will fall downwards due to gravity. Therefore, it is not a random experiment.

Answer: (d) Throwing a stone from a roof of a building.

Question 6

What is the probability of choosing a vowel from the alphabets?

$\frac{21}{26}$
$\frac{5}{26}$
$\frac{1}{26}$
$\frac{3}{26}$

Solution: To find the probability of choosing a vowel, we need to know the number of vowels and the total number of letters in the English alphabet. There are 26 letters in the English alphabet. The vowels are A, E, I, O, U. So, there are 5 vowels.

The formula for probability is:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the favorable outcomes are the vowels, and the total possible outcomes are all the letters of the alphabet.

$Probability = \frac{5}{26}$

Answer: (b) $\frac{5}{26}$

Common mistakes

Confusing the height of a histogram rectangle with class limits instead of frequency.
Incorrectly calculating the range by not identifying the absolute highest and lowest values.
Misunderstanding the definition of a random experiment.
Errors in counting favorable outcomes or total outcomes when calculating probability.

Revision tips

Review the definitions of histogram, pie chart, and range.
Practice calculating the range for various datasets.
Understand the conditions that define a random experiment.
Work through the probability examples to solidify the concept of favorable outcomes over total outcomes.

Practice MCQs

Q1. In a histogram, what does the height of each rectangle primarily represent?

Q2. Which type of chart is best suited for showing the relationship between a whole and its constituent parts?

Q3. What is the total angle at the center of a circle used in a pie chart?

Q4. Calculate the range of the data set: 20, 26, 28, 30, 46, 55, 56, 56, 60, 61.

Q5. Which of the following is NOT considered a random experiment?

Q6. What is the probability of selecting a vowel from the English alphabet?

Frequently asked questions

What is a histogram in the context of data handling?

A histogram is a graphical representation where the height of each rectangle corresponds to the frequency of the data within a specific class interval. It's used to visualize the distribution of numerical data.

How is a pie chart different from a histogram?

A pie chart represents data as slices of a circle, showing the proportion of each category to the whole. A histogram uses adjacent rectangles to show the frequency distribution of continuous data.

How do you calculate the range of a data set?

The range of a data set is calculated by subtracting the lowest value from the highest value in the set. It gives a measure of the spread of the data.

What is a random experiment?

A random experiment is an action or process where the outcome cannot be predicted with certainty, but the set of all possible outcomes is known. Examples include tossing a coin or rolling a die.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.

How can these NCERT Solutions help with exam preparation?

These solutions provide clear, step-by-step explanations for each question, helping students understand the concepts of data handling, probability, and graphical representation, which are crucial for exam success.

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