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 1 of 4

1. Q1 NCERT · Exercise 13.1
   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. Which method did you use for finding the mean, and why?

   Number of plants in 20 houses

   Number of plants	Number of houses
   0 - 2	1
   2 - 4	2
   4 - 6	1
   6 - 8	5
   8 - 10	6
   10 - 12	2
   12 - 14	3

   Show answer

   Mean $=\frac{162}{20}=8.1$ plants per house. Method: the direct method, chosen because the class marks and frequencies are small numbers, making $f_i{x}_i$ easy to evaluate exactly.

   Step-by-step solution →
2. Q2 NCERT · Exercise 13.1
   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 of 50 workers of a factory

   Daily wages (in Rs)	Number of workers
   500 - 520	12
   520 - 540	14
   540 - 560	8
   560 - 580	6
   580 - 600	10

   Show answer

   Mean daily wage $=$ Rs $545.20$.

   Step-by-step solution →
3. Q3 NCERT · Exercise 13.1
   The following distribution ​shows ​the daily pocket ​allowance of children ​of a ​locality. The mean pocket allowance ​is Rs 18. Find the missing ​frequency $f$.

   Daily pocket allowance of children

   Daily pocket allowance (in Rs)	Number of children
   11 - 13	7
   13 - 15	6
   15 - 17	9
   17 - 19	13
   19 - 21	$f$
   21 - 23	5
   23 - 25	4

   Show answer

   The missing frequency is $f=20$.

   Step-by-step solution →
4. Q4 NCERT · Exercise 13.1
   Thirty ​women ​were examined ​in ​a hospital by a ​doctor and the number of heartbeats per ​minute were recorded and summarised ​in the table below. Find the mean heartbeats per minute for these women, choosing a suitable method.

   Heartbeats per minute of 30 women

   Number of heartbeats per minute	Number of women
   65 - 68	2
   68 - 71	4
   71 - 74	3
   74 - 77	8
   77 - 80	7
   80 - 83	4
   83 - 86	2

   Show answer

   $\bar{x}=75.9$ heartbeats per minute (step-deviation method).

   Step-by-step solution →
5. Q5 NCERT · Exercise 13.1
   In a retail market, fruit vendors were selling mangoes kept in packing boxes. ​These boxes contained varying ​number of mangoes. The ​following was the distribution of mangoes according to the number of boxes. Find the mean number of ​mangoes kept ​in a packing box. Which method ​of finding the mean ​did ​you choose?

   Mangoes per box vs. number of boxes

   Number of mangoes	Number of boxes
   50 - 52	15
   53 - 55	110
   56 - 58	135
   59 - 61	115
   62 - 64	25

   Show answer

   $\bar{x}\approx 57.19$ mangoes per box, found by the step-deviation method.

   Step-by-step solution →
6. Q6 NCERT · Exercise 13.1
   The following data gives the ​distribution of total monthly ​household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, ​find the ​mean monthly expenditure.

   1. (i)Find the modal monthly expenditure of the families.
   2. (ii)Find ​the mean ​monthly expenditure of the ​families.

   Total monthly household expenditure of 200 families

   Expenditure (in Rs)	Number of families
   1000 - 1500	24
   1500 - 2000	40
   2000 - 2500	33
   2500 - 3000	28
   3000 - 3500	30
   3500 - 4000	22
   4000 - 4500	16
   4500 - 5000	7

   Show answer

   Modal monthly expenditure $\approx$ Rs $1847.83$; mean monthly expenditure $=$ Rs $2662.50$.

   Step-by-step solution →
7. Q7 NCERT · Exercise 13.1
   To find out ​the concentration of $S{O}_2$ in the ​air (in parts per million, i.e., ​ppm), ​the ​data was collected for 30 localities in a certain city and is presented ​below. Find the mean concentration of $S{O}_2$ in ​the air.

   Concentration of SO₂ in the air for 30 localities

   Concentration of SO${}_2$ (in ppm)	Frequency
   0.00 - 0.04	4
   0.04 - 0.08	9
   0.08 - 0.12	9
   0.12 - 0.16	2
   0.16 - 0.20	4
   0.20 - 0.24	2

   Show answer

   The mean concentration of $S{O}_2$ is $\bar{x}=\frac{2.96}{30}\approx 0.099$ ppm.

   Step-by-step solution →
8. Q8 NCERT · Exercise 13.1
   A class teacher has ​the ​following ​absentee record ​of 40 students of a class ​for the ​whole term. Find ​the mean number of days ​a student was absent.

   Absentee record of 40 students

   Number of days	Number of students
   0 - 6	11
   6 - 10	10
   10 - 14	7
   14 - 20	4
   20 - 28	4
   28 - 38	3
   38 - 40	1

   Show answer

   Mean number of days absent $=\frac{499}{40}=12.475\approx 12.48$ days.

   Step-by-step solution →
9. Q9 NCERT · Exercise 13.1
   The following table gives ​the literacy ​rate (in percentage) of ​35 ​cities. ​Find the ​mean literacy rate.

   Literacy rate of 35 cities

   Literacy rate (in %)	Number of cities
   45 - 55	3
   55 - 65	10
   65 - 75	11
   75 - 85	8
   85 - 95	3

   Show answer

   $\bar{x}\approx 69.43\%$ (step-deviation method).

   Step-by-step solution →
10. Q10 NCERT · Exercise 13.2
    The following table shows the ​ages of the ​patients admitted in a hospital during a year. Find the mode and ​the ​mean of ​the data ​given above. Compare and interpret the two measures of ​central tendency.

    Ages of patients admitted

    Age (in years)	Number of patients
    5 - 15	6
    15 - 25	11
    25 - 35	21
    35 - 45	23
    45 - 55	14
    55 - 65	5

    Show answer

    Mode $\approx 36.8$ years and Mean $\approx 35.38$ years. The most common and the average ages are both about $36$ years, so a typical patient is in the mid-thirties.

    Step-by-step solution →
11. Q11 NCERT · Exercise 13.2
    The following data gives the information ​on ​the observed ​lifetimes (in hours) of 225 electrical components. ​Determine the modal lifetimes of ​the ​components.

    Observed lifetimes of electrical components

    Lifetimes (in hours)	Frequency
    0 - 20	10
    20 - 40	35
    40 - 60	52
    60 - 80	61
    80 - 100	38
    100 - 120	29

    Show answer

    Modal lifetime $=65.625$ hours.

    Step-by-step solution →
12. Q12 NCERT · Exercise 13.2
    The ​table below shows the daily expenditure on food ​of 25 households in ​a locality. Find ​the ​mean daily expenditure on food ​by a suitable method.

    Daily expenditure on food of 25 households

    Daily expenditure (in Rs)	Number of households
    100 - 150	4
    150 - 200	5
    200 - 250	12
    250 - 300	2
    300 - 350	2

    Show answer

    Mean daily expenditure on food $=$ Rs $211$.

    Step-by-step solution →
13. Q13 NCERT · Exercise 13.2
    The following distribution gives ​the state-wise ​teacher-student ratio in higher secondary schools ​of India. ​Find ​the mode ​and mean of ​this data. Interpret the two measures.

    State-wise teacher-student ratio in higher secondary schools of India

    Number of students per teacher	Number of states / U.T.
    15 - 20	3
    20 - 25	8
    25 - 30	9
    30 - 35	10
    35 - 40	3
    40 - 45	0
    45 - 50	0
    50 - 55	2

    Show answer

    Mode $\approx 30.6$ and Mean $\approx 29.2$ students per teacher. Most states have a ratio near $30.6$, while the average ratio across states is about $29.2$.

    Step-by-step solution →
14. Q14 NCERT · Exercise 13.2
    The given distribution shows the number of ​runs ​scored by some top batsmen of the world ​in ​one-day international cricket matches. Find the ​mode ​of ​the data.

    Runs scored by top batsmen in ODIs

    Runs scored	Number of batsmen
    3000 - 4000	4
    4000 - 5000	18
    5000 - 6000	9
    6000 - 7000	7
    7000 - 8000	6
    8000 - 9000	3
    9000 - 10000	1
    10000 - 11000	1

    Show answer

    $\text{Mode}\approx 4608.7$ runs.

    Step-by-step solution →
15. Q15 NCERT · Exercise 13.2
    A student noted the number of ​cars passing through a spot on ​a road for 100 periods ​each of 3 minutes and summarised it in the table ​given below. Find the mode of ​the ​data.

    Number of cars passing in 100 three-minute periods

    Number of cars	Frequency
    0 - 10	7
    10 - 20	14
    20 - 30	13
    30 - 40	12
    40 - 50	20
    50 - 60	11
    60 - 70	15
    70 - 80	8

    Show answer

    Mode $\approx 44.7$ cars per 3-minute period.

    Step-by-step solution →
16. Q16 Exemplar · Exercise 13.1
    In the formula $\bar{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$, ​for finding ​the ​mean ​of grouped ​data $d_i$'s are ​deviations from $a$ of

    1. (a)lower limits of the classes
    2. (b)upper limits of the classes
    3. (c)mid points of the classes
    4. (d)frequencies of the class marks
    Show answer

    (c) mid points of the classes

    Step-by-step solution →
17. Q17 Exemplar · Exercise 13.1
    While computing mean ​of grouped ​data, ​we assume ​that the frequencies ​are

    1. (a)evenly distributed over all the classes
    2. (b)centred at the classmarks of the classes
    3. (c)centred at the upper limits of the classes
    4. (d)centred at the lower limits of the classes
    Show answer

    (b) centred at the classmarks of the classes

    Step-by-step solution →
18. Q18 Exemplar · Exercise 13.1
    If $x_i$'s are the mid points of ​the ​class intervals of grouped data, $f_i$'s are ​the ​corresponding frequencies ​and $\bar{x}$ is the mean, ​then $\sum (f_i{x}_i-\bar{x})$ ​is equal to

    1. (a)$0$
    2. (b)$-1$
    3. (c)$1$
    4. (d)$2$
    Show answer

    (a) $0$

    Step-by-step solution →
19. Q19 Exemplar · Exercise 13.1
    In ​the ​formula $\bar{x}=a+h\frac{\sum f_i{u}_i}{\sum f_i}$, ​for finding ​the mean ​of ​grouped frequency distribution, $u_i=$

    1. (a)$\frac{x_i+a}{h}$
    2. (b)$h(x_i-a)$
    3. (c)$\frac{x_i-a}{h}$
    4. (d)$\frac{a-x_i}{h}$
    Show answer

    (c) $\frac{x_i-a}{h}$

    Step-by-step solution →
20. Q20 Exemplar · Exercise 13.1
    The abscissa of ​the point of intersection of ​the less ​than type and ​of the more than type cumulative frequency curves of a ​grouped data ​gives ​its

    1. (a)mean
    2. (b)median
    3. (c)mode
    4. (d)all the three above
    Show answer

    (b) median

    Step-by-step solution →