Class 10 Maths · Chapter 13

Statistics

61 Class 10 Maths questions on Statistics from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

NCERT exercises

Exercise 13.1 (9) Exercise 13.2 (6) Exercise 13.3 (0)

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 4

Q21 Exemplar · Exercise 13.1
For the following distribution, the sum of lower limits of the median class and modal class is
Class-frequency distribution
Class Frequency
0 - 5 10
5 - 10 15
10 - 15 12
15 - 20 20
20 - 25 9
1. (a) $15$
2. (b) $25$
3. (c) $30$
4. (d) $35$
Show answer

(b) $25$

Step-by-step solution →
Q22 Exemplar · Exercise 13.1
Consider the following frequency distribution. The upper limit of the median class is
Frequency distribution
Class Frequency
0 - 5 13
6 - 11 10
12 - 17 15
18 - 23 8
24 - 29 11
1. (a)17
2. (b)17.5
3. (c)18
4. (d)18.5
Show answer

(b) 17.5

Step-by-step solution →
Q23 Exemplar · Exercise 13.1
For the following distribution, the modal class is
Cumulative marks distribution
Marks Number of students
Below 10 3
Below 20 12
Below 30 27
Below 40 57
Below 50 75
Below 60 80
1. (a) $10$ - $20$
2. (b) $20$ - $30$
3. (c) $30$ - $40$
4. (d) $50$ - $60$
Show answer

(c) $30$ - $40$

Step-by-step solution →
Q24 Exemplar · Exercise 13.1
Consider the following frequency distribution. The difference of the upper limit of the median class and the lower limit of the modal class is
Class-frequency distribution
Class Frequency
65 - 85 4
85 - 105 5
105 - 125 13
125 - 145 20
145 - 165 14
165 - 185 7
185 - 205 4
1. (a) $0$
2. (b) $19$
3. (c) $20$
4. (d) $38$
Show answer

(c) $20$

Step-by-step solution →
Q25 Exemplar · Exercise 13.1
The times, in seconds, taken by $150$ athletes to run a $110$ m hurdle race are tabulated below. The number of athletes who completed the race in less than 14.6 seconds is
Times of 150 athletes in a 110 m hurdle race
Class (seconds) Frequency
13.8 - 14 2
14 - 14.2 4
14.2 - 14.4 5
14.4 - 14.6 71
14.6 - 14.8 48
14.8 - 15 20
1. (a) $11$
2. (b) $71$
3. (c) $82$
4. (d) $130$
Show answer

(c) $82$

Step-by-step solution →

Class-frequency distribution
Class	Frequency
0 - 5	10
5 - 10	15
10 - 15	12
15 - 20	20
20 - 25	9

Frequency distribution
Class	Frequency
0 - 5	13
6 - 11	10
12 - 17	15
18 - 23	8
24 - 29	11

Cumulative marks distribution
Marks	Number of students
Below 10	3
Below 20	12
Below 30	27
Below 40	57
Below 50	75
Below 60	80

Class-frequency distribution
Class	Frequency
65 - 85	4
85 - 105	5
105 - 125	13
125 - 145	20
145 - 165	14
165 - 185	7
185 - 205	4

Times of 150 athletes in a 110 m hurdle race
Class (seconds)	Frequency
13.8 - 14	2
14 - 14.2	4
14.2 - 14.4	5
14.4 - 14.6	71
14.6 - 14.8	48
14.8 - 15	20

Q26 Exemplar · Exercise 13.1

Consider the following distribution: the frequency of the class 30-40 is

Cumulative ('more than') distribution
Marks obtained	Number of students
More than or equal to 0	63
More than or equal to 10	58
More than or equal to 20	55
More than or equal to 30	51
More than or equal to 40	48
More than or equal to 50	42

(a)3
(b)4
(c)48
(d)51

Show answer

(a) 3

Step-by-step solution →

Q27 Exemplar · Exercise 13.2

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.

Show answer

No, the statement is not correct. The grouped median uses an interpolation that assumes uniform spread within the median class, so it is only an estimate and generally differs from the exact ungrouped median.

Step-by-step solution →
Q28 Exemplar · Exercise 13.2

In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula $\overset{x}{ˉ} = a + \frac{\sum f _{i} d _{i}}{\sum f _{i}}$ where $a$ is the assumed mean. $a$ must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.

Show answer

No, the statement is not correct. The assumed mean $a$ can be any convenient number; it need not be one of the class mid-points, because $a$ cancels out and the final mean is unchanged.

Step-by-step solution →
Q29 Exemplar · Exercise 13.2

Is it true to say that the mean, mode and median of grouped data will always be different? Justify your answer.

Show answer

No, it is not true. For a symmetric grouped distribution the mean, median and mode are all equal, so they need not always be different.

Step-by-step solution →
Q30 Exemplar · Exercise 13.2

Will the median class and modal class of grouped data always be different? Justify your answer.

Show answer

No, they need not always be different. For the distribution with frequencies 2, 8, 2 over classes 0-10, 10-20, 20-30, the class 10-20 is both the modal class and the median class.

Step-by-step solution →
Q31 CBSE 2026
While calculating mean of a grouped frequency distribution, step deviation method was used $(\frac{x - a}{h} = u)$ . It was found that $\overset{x}{ˉ} = 64$ , $h = 5$ and $a = 62.5$ . The value of $\overset{u}{ˉ}$ is
1. (a) $0.5$
2. (b) $1.5$
3. (c) $0.3$
4. (d) $7.5$
Show answer

(c) $0.3$

Step-by-step solution →
Q32 CBSE 2026
While calculating mean of a grouped frequency distribution using step deviation method $(u = \frac{x - a}{h})$ it was found that $\overset{x}{ˉ} = 62$ , $a = 47.5$ , $h = 5$ . The value of $\overset{u}{ˉ}$ is:
1. (a) $3$
2. (b) $14.5$
3. (c) $2.9$
4. (d) $3.1$
Show answer

(c) $2.9$

Step-by-step solution →
Q33 CBSE 2026
The median and mode of a distribution are $25.2$ and $26.1$ respectively. The mean of the distribution is :
1. (a) $24.75$
2. (b) $24.25$
3. (c) $24.3$
4. (d) $25.5$
Show answer

(a) $24.75$

Step-by-step solution →
Q34 CBSE 2026
If for a frequency distribution, the mean is $\frac{3}{4}$ times the median, then mode is :
1. (a)equal to median
2. (b) $\frac{3}{2}$ times the median
3. (c)equal to mean
4. (d) $3$ times the mean
Show answer

(b) $\frac{3}{2}$ times the median

Step-by-step solution →
Q35 CBSE 2026
Let ' $a$ ' be the assumed mean and ' $h$ ' be the class size for a grouped data. Which of the following is not the correct formula to find the mean of the grouped data ?
1. (a) $\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}$
2. (b) $\overset{x}{ˉ} = a + \frac{\sum f _{i} d _{i}}{\sum f _{i}}$ , where $d_{i} = x_{i} - a$
3. (c) $\overset{x}{ˉ} = a + \frac{\sum f _{i} u _{i}}{\sum f _{i}}$ , where $u_{i} = \frac{x _{i} - a}{h}$
4. (d) $\overset{x}{ˉ} = a + \frac{\sum f _{i} y _{i}}{\sum f _{i}} \times h$ , where $y_{i} = \frac{x _{i} - a}{h}$
Show answer

(c) $\overset{x}{ˉ} = a + \frac{\sum f _{i} u _{i}}{\sum f _{i}}$ , where $u_{i} = \frac{x _{i} - a}{h}$

Step-by-step solution →
Q36 CBSE 2026
If the mean and mode of a data are $12$ and $21$ respectively, then its median is :
1. (a) $6$
2. (b) $13.5$
3. (c) $15$
4. (d) $14$
Show answer

(c) $15$

Step-by-step solution →
Q37 CBSE 2026
The mean and median of a frequency distribution are $43$ and $43.4$ respectively. The mode of the distribution is :
1. (a) $43.4$
2. (b) $42.4$
3. (c) $44.2$
4. (d) $49.3$
Show answer

(c) $44.2$

Step-by-step solution →
Q38 CBSE 2026
The upper limit of the median class of the above data is :
Class 0-10 10-20 20-30 30-40 40-50
Frequency 3 5 7 9 11
1. (a) $10$
2. (b) $20$
3. (c) $30$
4. (d) $40$
Show answer

(d) $40$

Step-by-step solution →
Q39 CBSE 2026
Consider the given data : The difference of lower limit of the median class and upper limit of the modal class is :
Class 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120
Frequency 15 30 50 63 35 32
1. (a) $0$
2. (b) $20$
3. (c) $40$
4. (d) $10$
Show answer

(b) $20$

Step-by-step solution →
Q40 CBSE 2026
Which of the following is affected by the extreme values in a given data ?
1. (a)Mean only
2. (b)Median only
3. (c)Mode only
4. (d)Mean and Mode both
Show answer

(a) Mean only

Step-by-step solution →