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Home / Boards / CBSE / Important Questions / Class 10 / Maths / Statistics

Class 10 Math Chapter 13
Statistics
Important Questions

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Here are some important questions for Class 10 Mathematics Chapter 13, Statistics, carefully selected to help students prepare effectively for the CBSE Class 10 Mathematics Examination in 2024-25. By practicing these diverse problems, students can improve their understanding of Statistics concepts and enhance their problem-solving abilities. These questions are designed to clarify doubts and contribute to better performance in the Statistics chapter.

Introduction

In Chapter 13 of Class 10 Mathematics,Statistics, we will focus on understanding and calculating the measures of central tendency—mean, median, and mode—for grouped data. These measures help us analyze and summarize large sets of data by providing insights into the typical values and trends within the data.

What is the purpose of statistics in mathematics?

Statistics involves collecting, analyzing, and interpreting data to understand trends, patterns, and information in various fields. It helps in making informed decisions and drawing conclusions.
cbse class 10 maths statistics important questions and answers

Class 10 Statistics Important Questions and Answers

Q1. In an inclusive series :
Options
(a) The lower class boundary is the same as the upper class boundary of the previous class.
(b) The upper class boundary is the same as the lower class boundary of the next class.
(c) Both the lower and upper class boundaries are the same.
(d) The lower and upper class boundaries are contained within the class and do not intersect with either the upper boundary of the previous class or the lower boundary of the next class.

Ans.(d)

Explanation:
The lower and upper class boundaries are contained within the class and do not intersect with either the upper boundary of the previous class or the lower boundary of the next class.

Q2. If the mean of observations x_1, \space x_2,\space ...... \space x_n is, \text{\={x}}, then the mean of ax_1, \space ax_2,\space ax_3,\space ......,\space ax_n\space is:
Option
(a)\space \text{ \={x}} \\[4.5 bp] (b)\space a + \text{\={x}} \\[4.5 bp] (c)\space a\text{\={x}} \\[4.5 bp] (d) None of these

Ans. (c) a \text{\={x}}

Explanation:
Mean of observations \space x_1 \space + \space x_2,\space …. \space x_n \space is \space \text{\={x}} \\ \space x_1 \space + \space x_2 \space + \space x_3 \space +, ….\space x_n = n \text{\={x}} \\[4.5 bp] ∴ \space x_1 + a + x_2 + a + x_3 + a + \space .......\space x_n + a \\[4.5 bp] =\space x_1 + x_2 + x_3 +,\space …. \space x_n + na
∴ Mean of \space (x_1+x_2+x_3+\space ....\space +x_n)+ na
\\[4.5 bp] = \dfrac{n\text{\={x}} + na}{n}= \text{\={x}} + a

Q3.The table below shows the distribution of marks obtained by students in an examination. Calculate the value of x if the mean mark is 18.
MarksNo. of students
56
104
156
2012
25x
304

Explanation:
Given Mean = 18

MarksNo. of studentsMid-value
(xi)(fi)fi × xi
5630
10440
15690
2012240
25x25x
304120
Total32 + x520 + 25x
\text{Mean =} \dfrac{\Sigma f_ix_i}{\Sigma f_i}\\[4.5 bp] \rArr \space 18 = \dfrac{520 + 25 x}{32 + x}\\[2.5 bp] ⇒ 18 (32 + x) = 520 + 25x
⇒ 576 + 18 x = 520 + 25x
⇒ 25x - 18x =576-520
⇒ 7x = 56
⇒ x = 8

Q4. Find the mean of the following frequency distribution:
Class IntervalFrequency
0-504
50-1008
100-15016
150-20013
200-2506
250-3003

Explanation:

Class Interval Frequency (fi )Class Marks (xi)(fi xi)
0-50425100
50-100875600
100-150161252000
150-200131752275
200-25062251350
250-3003275825
N = Σfi = 50(fi xi) =7150

Explanation:
Thus,
Mean = Σf_ix_i/Σf_i = 7150/50
= 143

Q5. The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure of food.

Explanation:

Daily Expenditure (in ₹ )No. of Households
(fi)		Mid-value
( xi)		fi × xi
100-1504125500
150-2005175875
200-250122252700
250-3002275550
300-3502325650
Σxi =25Σxi fi = 5275

Explanation:
\therefore \space \space \space \text{Mean } (\bar{x}) = \dfrac{\Sigma f_i \space x_i}{\Sigma f_i} = \dfrac{5275}{25} = 211\\[2.5 bp] Hence, Mean = 211

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CBSE Class 10 Maths Chapter wise Important Questions

making of global world class 10 important questions

Conclusion

To enhance your grasp of the Statistics chapter, consider exploring oswal.io. This website provides a variety of practice questions tailored to facilitate better learning. By engaging with these questions, you can reinforce your understanding of statistical concepts and improve your problem-solving abilities in this important math topic.

Frequently Asked Questions

Ans: Data refers to information or observations collected for analysis. Raw data is the original, unprocessed form of data before any organization or manipulation.
Ans: Statistics is a branch of mathematics that involves collecting, organizing, analyzing, interpreting, and presenting data. It provides methods for understanding patterns, trends, and relationships in data.
Ans: The median is the middle value of a dataset when arranged in ascending or descending order. It divides the data into two equal halves.
Ans: Grouped data is data that is categorized into intervals or classes. It simplifies data representation when dealing with large datasets.
Ans: The midpoint of a class interval is calculated by adding the lower and upper limits of the interval and dividing by 2.
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CBSE Important Questions Class 10

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