Chapter 13 · Statistics

NCERT Class 10 Maths Exercise 13.1

All 9 questions of NCERT Class 10 Maths Exercise 13.1 (Statistics), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   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
   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
   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
   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
   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
   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
   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
   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
   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 →