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Class 10 Math Chapter 13
Statistics
Important Questions

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.

Table of Contents

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.

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.

Marks	No. of students
5	6
10	4
15	6
20	12
25	x
30	4

Explanation:
Given Mean = 18

Marks	No. of students	Mid-value
(x_i)	(f_i)	f_i× x_i
5	6	30
10	4	40
15	6	90
20	12	240
25	x	25x
30	4	120
Total	32 + x	520 + 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 Interval	Frequency
0-50	4
50-100	8
100-150	16
150-200	13
200-250	6
250-300	3

Explanation:

Class Interval	Frequency (f_i )	Class Marks (x_i)	(f_i x_i)
0-50	4	25	100
50-100	8	75	600
100-150	16	125	2000
150-200	13	175	2275
200-250	6	225	1350
250-300	3	275	825
	N = Σf_i = 50		(f_i x_i) =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 (f_i)	Mid-value ( x_i)	f_i× x_i
100-150	4	125	500
150-200	5	175	875
200-250	12	225	2700
250-300	2	275	550
300-350	2	325	650
	Σx_i=25		Σx_if_i= 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

CBSE Class 10 Maths Chapter wise Important Questions

Chapter No.	Chapter Name
Chapter 1	Real Numbers
Chapter 2	Polynomials
Chapter 3	Pair of Linear Equations in Two Variable
Chapter 4	Quadratic Equations
Chapter 5	Arithmetic Progressions
Chapter 6	Triangles
Chapter 7	Coordinate Geometry
Chapter 8	Introduction to Trigonometry
Chapter 9	Some Applications of Trigonometry
Chapter 10	Circles
Chapter 11	Areas Related to Circle
Chapter 12	Surface Areas and Volumes
Chapter 13	Statistics
Chapter 14	Probability

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.

Chapter Wise Important Questions for CBSE Board Class 10 Maths
Real Numbers
Polynomials
Pair of Linear Equations in Two Variables
Quadratic Equations
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Some Applications of Trigonometry
Circles
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

Class 10 Math Chapter 13
Statistics
Important Questions

Introduction

What is the purpose of statistics in mathematics?

Class 10 Statistics Important Questions and Answers

Q1. In an inclusive series :

Options

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

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.

Q4. Find the mean of the following frequency distribution:

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

CBSE Class 10 Maths Chapter wise Important Questions

Conclusion

Frequently Asked Questions

Q1 : Define 'data' and 'raw data.

Q2 : What is statistics?

Q3 : Define median.

Q4 : Explain the concept of 'grouped data’.

Q5: How is the 'midpoint' of a class interval calculated?

Class 10 Math Chapter 13 Statistics Important Questions

Introduction

What is the purpose of statistics in mathematics?

Class 10 Statistics Important Questions and Answers

Q1. In an inclusive series :

Options

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

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.

Q4. Find the mean of the following frequency distribution:

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

CBSE Class 10 Maths Chapter wise Important Questions

Conclusion

Frequently Asked Questions

Q1 : Define 'data' and 'raw data.

Q2 : What is statistics?

Q3 : Define median.

Q4 : Explain the concept of 'grouped data’.

Q5: How is the 'midpoint' of a class interval calculated?

Class 10 Math Chapter 13
Statistics
Important Questions

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:

$(a)\space \text{ \={x}} \\[4.5 bp] (b)\space a + \text{\={x}} \\[4.5 bp] (c)\space a\text{\={x}} \\[4.5 bp]$ (d) None of these