NCERT Solutions for Class 10 Maths Chapter 13

NCERT Solutions for Class 10 Maths Chapter 13 Statistics

Exercise 13.1

Question 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.

Thank you for reading this post, don't forget to subscribe!

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

Which method did you use for finding the mean, and why?

Answer
To find the mean value, we will use the direct method because the numerical value of f_i and x_i are small.

C.I.	f	x	fx
0-2	1	1	1
2-4	2	3	6
4-6	1	5	5
6-8	5	7	35
8-10	6	9	54
10-12	2	11	22
12-14	3	13	39
Total	20		162

Mean, \(\bar{x}\) = \(\frac{\sum fx}{\sum f}\) = \(\frac{162}{20}\) = 8.1

---

---

Question 2:
Consider the following distribution of daily wages of 50 workers of a factory.

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

Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer

C.I.	f	x	d = \(\frac{x – 550}{20}\)	fd
500-520	12	510	-2	-24
520-540	14	530	-1	-14
540-560	8	A = \(\ {550}\)	0	0
560-580	6	570	+1	+6
580-600	10	590	+2	+20
Total	50			-12

Mean, \(\bar{x}\) = A + \(\frac{\sum{fd}}{\sum{f}} \times h\)
\(\quad\) \(\quad\) \(\quad\) = 550 + \(\frac{-12}{50} \times 20\)
\(\quad\) \(\quad\) \(\quad\) = 550 + \(\frac{-240}{50} \)
\(\quad\) \(\quad\) \(\quad\) = 550 – 4.8
\(\quad\) \(\quad\) \(\quad\) = 545.20

---

Question 3:
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 (in ₹)	11-13	13-15	15-17	17-19	19-21	21-23	23-25
Number of Children	7	6	9	13	f	5	4

Answer

C.I.	f	x	fx
11-13	7	12	84
13-15	6	14	84
15-17	9	16	144
17-19	13	18	234
19-21	f	20	20f
21-23	5	22	110
23-25	4	24	96
Total	44 + f		752 + 20f

Mean, \(\bar{x}\) = \(\frac{\sum{fx}}{\sum{f}}\)
\(\quad\) \(\quad\) 18 = \(\frac{752 + 20f}{44 + f}\)
\(\quad\) \(\quad\) 752 + 20f =18 (44 + f)
\(\quad\) \(\quad\) 752 + 20f = 792 + 18f
\(\quad\) \(\quad\) 20f – 18f = 792 -752 = 40
\(\quad\) \(\quad\) 2f = \(\frac{40}{2}\) = 20
\(\quad\) \(\quad\) f = 20

---

---

Question 4:
Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.

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

Answer

C.I.	f	x	d = \(\frac{x – 75.5}{3}\)	fd
65-68	2	66.5	-3	-6
68-71	4	69.5	-2	-8
71-74	3	72.5	-1	-3
74-77	8	75.5 =A	0	0
77-80	7	78.5	+1	+7
80-83	4	81.5	+2	+8
83-86	2	84.5	+3	+6
Total	30			4

Mean, \(\bar{x}\) = A + \(\frac{\sum{fd}}{\sum{f}} \times h\)
\(\quad\) \(\quad\) \(\quad\) = 75.5 + \(\frac{4}{30} \times 3\)
\(\quad\) \(\quad\) \(\quad\) = 75.5 + \(\frac{12}{30} \)
\(\quad\) \(\quad\) \(\quad\) = 75.5 + 0.4
\(\quad\) \(\quad\) \(\quad\) = 75.9

Question 5:
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.

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

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Question 6:
The table below shows the daily expenditure on food of 25 households in a locality.

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

Find the mean daily expenditure on food by a suitable method.

Question 7:
To find out the concentration of SO₂ 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:

Concentration of SO2 (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

Find the mean concentration of SO₂ in the air.

Question 8:
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.

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

Question 9:
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

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