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.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 3 of 4

1. Q41 CBSE 2026
   Mean and Median ​of a frequency distribution are $43$ and $40$ ​respectively. ​The ​value ​of ​mode is

   1. (a)$34$
   2. (b)$43$
   3. (c)$38.5$
   4. (d)$41.5$
   Show answer

   (a) $34$

   Step-by-step solution →
2. Q42 CBSE 2026
   If ​for a ​data, median is $5$ and ​mode is $4$, ​then ​mean is equal ​to ​:

   1. (a)$7$
   2. (b)$11$
   3. (c)$\frac{11}{2}$
   4. (d)$\frac{14}{3}$
   Show answer

   (c) $\frac{11}{2}$

   Step-by-step solution →
3. Q43 CBSE 2026
   In the ​following ​question, a statement of ​Assertion (A) is followed by ​a statement of Reason (R). ​Choose ​the correct ​option.

   Assertion (A): If the value of mode and mean for a distribution is $50$ and $56$ respectively, then the value of median is $54$.

   Reason (R): $\text{Median}=\frac{1}{3}\left(\text{Mode}-2\text{Mean}\right)$

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (c) Assertion (A) is true, but Reason (R) is false.

   Step-by-step solution →
4. Q44 CBSE 2026
   A statement of ​Assertion (A) is followed ​by a ​statement of ​Reason ​(R). ​Choose the correct option.

   Assertion (A): The mean of first '$n$' natural numbers is $\frac{n-1}{2}$.

   Reason (R): The sum of first '$n$' natural numbers is $\frac{n(n+1)}{2}$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (d) Assertion (A) is false, but Reason (R) is true.

   Step-by-step solution →
5. Q45 CBSE 2026
   Direction: In the following ​question, a statement ​of Assertion ​(A) ​is followed by ​a statement of Reason (R). Choose ​the correct ​option.

   Assertion (A): Median of a data is the value of $\frac{N}{2}$, where $N$ represents sum of all frequencies.

   Reason (R): Median divides the whole distribution in two equal parts.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer

   (d) Assertion (A) is false but Reason (R) is true.

   Step-by-step solution →
6. Q46 CBSE 2026
   In the following question, a statement ​of Assertion ​(A) is ​followed by ​a ​statement ​of Reason (R). Choose ​the correct ​option.

   Assertion (A): If the Mode and Mean of a data are $12k$ and $15k$, then Median of the data is $14k$.

   Reason (R): The relation between the Mean, Mode and Median of a data is : $\text{Mean}=3\text{Median}-2\text{Mode}$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (c) Assertion (A) is true, but Reason (R) is false.

   Step-by-step solution →
7. Q47 CBSE 2026
   Find the ​mean ​of ​the ​following distribution :

   Frequency distribution

   Class	Frequency
   30 - 40	6
   40 - 50	13
   50 - 60	8
   60 - 70	12
   70 - 80	11

   Show answer

   The mean of the distribution is $56.8$.

   Step-by-step solution →
8. Q48 CBSE 2026
   The median of the following ​data is $137$. Find the ​values of $x$ and $y$, ​given that ​total of ​frequencies ​is $68$.

   Class-frequency distribution

   Class	Frequency
   65 - 85	4
   85 - 105	5
   105 - 125	$x$
   125 - 145	20
   145 - 165	14
   165 - 185	$y$
   185 - 205	4

   Show answer

   $x=13$ and $y=8$.

   Step-by-step solution →
9. Q49 CBSE 2026
   Find mean and ​mode ​of the following ​distribution ​:

   Frequency distribution

   Class	Frequency
   0 - 10	3
   10 - 20	6
   20 - 30	11
   30 - 40	10
   40 - 50	13
   50 - 60	3
   60 - 70	4

   Show answer

   Mean $=34.8$ and Mode $=40+\frac{30}{13}\approx 42.31$.

   Step-by-step solution →
10. Q50 CBSE 2026
    The mean ​of the ​following frequency distribution is $28$. If ​sum of all ​frequencies ​is $100$, then ​find ​the values of $p$ and $q$ :

    Frequency distribution with unknown frequencies p and q (mean = 28, total frequency = 100)

    Class Interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
    Frequency	12	$p$	27	20	$q$	6

    Show answer

    The missing frequencies are $p=18$ and $q=17$.

    Step-by-step solution →
11. Q51 CBSE 2026
    Find ​median ​and ​mode ​of the ​following ​distribution :

    Grouped frequency distribution

    Class Interval	Frequency
    0 - 15	15
    15 - 30	10
    30 - 45	12
    45 - 60	9
    60 - 75	8
    75 - 90	10
    90 - 105	6

    Show answer

    Median $=42.5$ and Mode $=11.25$.

    Step-by-step solution →
12. Q52 CBSE 2026
    The ​mean ​of the following ​frequency distribution ​is $35$. ​Find the values ​of $x$ and $y$, ​if the sum of frequencies is $25$ :

    Class	Frequency
    0-10	1
    10-20	$x$
    20-30	5
    30-40	7
    40-50	$y$
    50-60	3
    60-70	1

    Show answer

    The missing frequencies are $x=3$ and $y=5$.

    Step-by-step solution →
13. Q53 CBSE 2026
    An ​SBI health insurance agent found the following ​data ​for distribution of ages of $100$ policy holders. The health ​insurance policies ​are given to persons ​of age $15$ years and onwards, but less than $60$ ​years. Find the modal age and median age of the policy holders.

    Age (in yrs)	Number of policy holders
    15 – 20	2
    20 – 25	4
    25 – 30	18
    30 – 35	21
    35 – 40	33
    40 – 45	11
    45 – 50	3
    50 – 55	6
    55 – 60	2

    Show answer

    The modal age of the policy holders is $35+\frac{30}{17}\approx 36.76$ years and the median age is $35+\frac{25}{33}\approx 35.76$ years.

    Step-by-step solution →
14. Q54 CBSE 2026
    Find mean and mode ​of ​the ​following ​data:

    Frequency distribution

    Class	Frequency
    10 - 20	5
    20 - 30	4
    30 - 40	10
    40 - 50	13
    50 - 60	12
    60 - 70	10
    70 - 80	6

    Show answer

    Mean $\approx 47.83$ and Mode $=47.5$.

    Step-by-step solution →
15. Q55 CBSE 2026
    Find the ​mean and the ​mode for the ​following ​frequency distribution ​:

    Frequency distribution

    Class	30 - 35	35 - 40	40 - 45	45 - 50	50 - 55
    Frequency	3	9	7	3	2

    Show answer

    Mean $\approx 40.83$ and Mode $=38.75$.

    Step-by-step solution →
16. Q56 CBSE 2026
    The mode ​of the ​following ​data is $3.286$ ​: Find the mean and median ​of ​the above ​data.

    Family size	1-3	3-5	5-7	7-9	9-11
    Number of families	7	8	2	2	1

    Show answer

    Mean $=4.2$ and Median $=3.75$.

    Step-by-step solution →
17. Q57 CBSE 2026
    The ​median ​of the ​following data ​is $525$. ​If the ​sum of all the frequencies is $100$, find ​the values of $p$ and $q$.

    Class	Frequency
    0 - 100	2
    100 - 200	$p$
    200 - 300	9
    300 - 400	12
    400 - 500	17
    500 - 600	20
    600 - 700	15
    700 - 800	9
    800 - 900	$q$
    900 - 1000	4

    Show answer

    The values are $p=5$ and $q=7$.

    Step-by-step solution →
18. Q58 CBSE 2026
    The following ​table ​shows ​the weight ​(in ​kg) of $40$ students of class X : Find ​the mean weight ​and median weight.

    Weight (in kg)	Number of students
    40 - 45	3
    45 - 50	4
    50 - 55	10
    55 - 60	8
    60 - 65	8
    65 - 70	4
    70 - 75	3

    Show answer

    The mean weight is $57.25$ kg and the median weight is $56.875$ kg.

    Step-by-step solution →
19. Q59 CBSE 2026
    The ​median of the ​following data ​is $50$ and the sum of ​all frequencies is $90$. ​Find the ​values of $p$ and $q$.

    Frequency distribution

    Class	Frequency
    20 - 30	$p$
    30 - 40	15
    40 - 50	25
    50 - 60	20
    60 - 70	$q$
    70 - 80	8
    80 - 90	10

    Show answer

    $p=5$ and $q=7$.

    Step-by-step solution →
20. Q60 CBSE 2026
    Find the mean ​and mode ​of ​the ​following ​distribution :

    Frequency distribution

    Class	0 - 15	15 - 30	30 - 45	45 - 60	60 - 75	75 - 90	90 - 105
    Frequency	4	8	11	14	10	7	6

    Show answer

    Mean $=53.25$ and Mode $\approx 51.43$.

    Step-by-step solution →