CBSE Class 10 Mathematics Chapter 14 Statistics NCERT Solutions

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

NCERT Solutions PDF Class 10 PDF

This chapter provides a detailed exploration of statistical concepts for Class 10 CBSE students. It covers methods to analyze data, focusing on calculating the mean, median, and mode of grouped data. The solutions offer step-by-step guidance for solving problems related to frequency distributions. Students will learn to identify appropriate methods for calculating the mean, such as the direct method, assumed mean method, and step-deviation method, based on the given data. Understanding these concepts is crucial for interpreting data effectively and is a key part of the Class 10 Mathematics syllabus, aiding students in their exam preparation and building a strong foundation in statistics.

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Quick info

Board	CBSE
Class	Class 10
Subject	Mathematics
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 14: Statistics

Chapter summary

Chapter 14, Statistics, for Class 10 Mathematics NCERT Solutions focuses on understanding and calculating measures of central tendency for grouped data. It covers the calculation of the mean using direct, assumed mean, and step-deviation methods. The solutions provide clear steps and explanations for each method, enabling students to solve problems related to frequency distributions and interpret statistical data effectively for their exams.

Learning outcomes

Understand the concept of statistics and its application in real life.
Calculate the mean of grouped data using the direct method.
Determine the class mark for a given class interval.
Apply the assumed mean method for calculating the mean of grouped data.
Choose an appropriate method for calculating the mean based on the data.
Interpret the results of statistical calculations in the context of the problem.

Topics covered

Paper topics

Statistics
Mean of Grouped Data
Class Interval
Frequency
Class Mark
Direct Method
Assumed Mean Method
Step-Deviation Method
Data Analysis
Frequency Distribution

Important topics

Mean of Grouped Data
Direct Method for Mean
Assumed Mean Method for Mean
Step-Deviation Method for Mean
Class Mark Calculation
Appropriate Method Selection

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Questions and Solutions

Question 1

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Number of plants: 0 - 2, 2 - 4, 4 - 6, 6 - 8, 8 - 10, 10 - 12, 12 - 14

Number of houses: 1, 2, 1, 5, 6, 2, 3

Which method did you use for finding the mean, and why?

Solution:

To find the mean number of plants per house, we first need to calculate the class mark (x_i) for each class interval. The class mark is the midpoint of the interval and is calculated using the formula:

$x_i = \frac{\text{Upper limit} + \text{Lower limit}}{2}$

We will then calculate the product of each class mark (x_i) and its corresponding frequency (f_i), which is the number of houses. Finally, we will use the direct method to find the mean, as the values of class marks and frequencies are relatively small.

The calculations are summarized in the table below:

Number of plants (Class Interval)	Number of houses (f_i)	Class Mark (x_i)	$f_i x_i$
Number of plants (Class Interval)	Number of houses (f_i)	Class Mark (x_i)	$f_i x_i$	0 - 2	1	1	$1 \times 1 = 1$
2 - 4	2	3	$2 \times 3 = 6$
4 - 6	1	5	$1 \times 5 = 5$
6 - 8	5	7	$5 \times 7 = 35$
8 - 10	6	9	$6 \times 9 = 54$
10 - 12	2	11	$2 \times 11 = 22$
12 - 14	3	13	$3 \times 13 = 39$
Total	$\sum f_i = 20$		$\sum f_i x_i = 162$

From the table, we have:

\sum f_i = 20

\sum f_i x_i = 162

The mean (

\bar{x}

) is calculated using the direct method formula:

\bar{x} = \frac{\sum f_i x_i}{\sum f_i}

Substituting the values:

\bar{x} = \frac{162}{20} = 8.1

Therefore, the mean number of plants per house is 8.1.

The direct method was used because the class marks (x_i) and frequencies (f_i) were small, making the calculations straightforward.

Question 2

Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.

Daily wages (in Rs): 100 - 120, 120 - 140, 140 - 160, 160 - 180, 180 - 200

Number of workers: 12, 14, 10, 8, 6

Solution:

To find the mean daily wages, we first calculate the class mark (x_i) for each class interval using the formula:

$x_i = \frac{\text{Upper limit} + \text{Lower limit}}{2}$

The class size (h) for this data is 20 (e.g., 120 - 100 = 20).

Since the class marks and frequencies involve larger numbers, it is appropriate to use the assumed mean method or the step-deviation method to simplify calculations. Let's use the assumed mean method. We assume a mean (a) from the class marks. Let's choose a = 150.

We then calculate the deviation ( $d_i = x_i - a$ ) and the product $f_i d_i$ for each class.

Daily wages (Class Interval)	Number of workers (f_i)	Class Mark (x_i)	$d_i = x_i - a$	$f_i d_i$
100 - 120	12	110	$110 - 150 = -40$	$12 \times (-40) = -480$
120 - 140	14	130	$130 - 150 = -20$	$14 \times (-20) = -280$
140 - 160	10	150	$150 - 150 = 0$	$10 \times 0 = 0$
160 - 180	8	170	$170 - 150 = 20$	$8 \times 20 = 160$
180 - 200	6	190	$190 - 150 = 40$	$6 \times 40 = 240$
Total	$\sum f_i = 50$			$\sum f_i d_i = -480 - 280 + 0 + 160 + 240 = -360$

The mean (

\bar{x}

) using the assumed mean method is given by:

\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}

Substituting the values:

\bar{x} = 150 + \frac{-360}{50}

\bar{x} = 150 - 7.2

\bar{x} = 142.8

Thus, the mean daily wages of the workers is Rs 142.8.

Common mistakes

Incorrectly calculating the class mark (midpoint) of a class interval.
Errors in summing up the frequencies (Σf_i) or the products (Σf_i x_i).
Choosing an inappropriate method for calculating the mean, leading to complex calculations.
Mistakes in arithmetic operations, especially with larger numbers or fractions.

Revision tips

Practice calculating the mean using all three methods (direct, assumed mean, step-deviation) to understand when each is most suitable.
Pay close attention to correctly identifying the class intervals and their corresponding frequencies.
Double-check your calculations for class marks, deviations, and the final summation steps.
Review the formulas for each method and ensure you are applying them accurately.

Practice MCQs

Q1. What is the formula for calculating the class mark (x_i) of a class interval?

Q2. Which method is generally preferred for calculating the mean when class marks (x_i) and frequencies (f_i) are small?

Q3. In the assumed mean method, what does 'a' represent?

Q4. What is the class size (h) in the second question's data?

Frequently asked questions

What is the main focus of Chapter 14: Statistics for CBSE Class 10 Maths?

Chapter 14 focuses on understanding and calculating measures of central tendency, primarily the mean, for grouped data using different methods like the direct method, assumed mean method, and step-deviation method.

How do I calculate the mean for grouped data?

You can calculate the mean for grouped data using the direct method (Σf_i x_i / Σf_i), the assumed mean method (a + Σf_i d_i / Σf_i), or the step-deviation method (a + h * Σf_i u_i / Σf_i), depending on the data.

What is a class mark and how is it calculated?

A class mark is the midpoint of a class interval. It is calculated by adding the lower limit and upper limit of the interval and dividing the sum by 2.

When should I use the direct method versus the assumed mean or step-deviation method?

The direct method is best when the class marks and frequencies are small. The assumed mean and step-deviation methods are more convenient for larger values, as they simplify calculations.

Are these NCERT Solutions helpful for exam preparation?

Yes, these solutions provide clear, step-by-step explanations and cover the methods required for calculating statistical measures, which are essential for exam revision and understanding the concepts thoroughly.

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