RD Sharma Solutions for Class 10 Chapter 7 Statistics Exercise 7.3

RD Sharma Solutions Chapter 7 Statistics Exercise 7.3 Class 10 Maths

Chapter Name	RD Sharma Chapter 7 Statistics
Book Name	RD Sharma Mathematics for Class 10
Other Exercises	Exercise 7.1 Exercise 7.2 Exercise 7.4 Exercise 7.5 Exercise 7.6
Related Study	NCERT Solutions for Class 10 Maths

Exercise 7.3 Solutions

1. The following table gives the distribution of total household expenditure(in rupees) of manual workers in a city. 

Expenditure (in rupees)(x)	Frequency (fi)	Expenditure (in rupees)(xi)	Frequency(fi)
100 – 150	24	300 – 350	30
150 – 200	40	350- 400	22
200 – 250	33	400 – 450	16
250 – 300	28	450 -500	7

Find the average expenditure (in rupees) per household.

Solution

Let the assumed mean (A) = 275.

2. A survey was conducted by a group of students as a part of their environment awareness program, 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.

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 ?

Solution

3. Consider the following distribution of daily wages of 50 workers of a factory

Daily wages(in Rs.)	100 – 120	120 – 140	140 – 160	160 – 180	180 – 200
Number of workers :	12	14	8	6	10

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

Solution

Let the assume mean (A) = 150 

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

Number of heat	65 – 68	68 – 71	71 – 74	74 – 77	77 – 80	80 – 83	83 – 86
Number of women:	2	4	3	8	7	4	2

Solution

5. Find the mean of each of the following frequency distributions: (5 – 14 )

Class interval :	0 – 6	6 – 12	12 – 18	18 – 24	24 – 30
Frequency:	6	8	10	9	7

Solution

6.

Class interval:	50 – 70	70 – 90	90 – 110	110 – 130	130 – 150	150 – 170
Frequency:	18	12	13	27	8	22

Solution

7.

Class interval:	0 – 8	8 – 16	16 – 24	24 – 32	32 – 40
Frequency:	6	7	10	8	9

Solution

8.

Class interval:	0 – 6	6 – 12	12 – 18	18 – 24	24 – 30
Frequency :	7	5	10	12	6

Solution

9.

Class interval :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency:	9	12	15	10	14

Solution

10.

Class interval :	0 – 8	8 – 16	16 – 24	24 – 32	32 – 40
Frequency:	5	9	10	8	8

Solution

11.

Class interval:	0 – 8	8 – 16	16 – 24	24 – 32	32 – 40
Frequency:	5	6	4	3	2

Solution

12.

Class interval:	10 – 30	30 – 50	50 – 70	70 – 90	90 – 110	110 – 130
Frequency:	5	8	12	20	3	2

Solution

13.

Class interval:	25 – 35	35 – 45	45 – 55	55 – 65	65 – 75
Frequency:	6	10	8	12	4

Solution

14.

Classes:	25 – 29	30 – 34	35 – 39	40 – 44	45 – 49	50 – 54	55 – 59
Frequency:	14	22	16	6	5	3	4

Solution

15. For the following distribution, calculate mean using all suitable methods:

Size of item:	1 -4	4 – 9	9 – 16	16 – 27
Frequency:	6	12	26	20

Solution

16. The weekly observations on cost of living index in a certain city for the year 2004 – 2005 are given below. Compute the weekly cost of living index.

Cost of living index	Number of Students	Cost of living index	Number of Students
1400 – 1500	5	1700 – 1800	9
1500 – 1600	10	1800 – 1900	6
1600 - 1700	20	1900 – 2000	2

Solution

17. The following table shows the marks scored by 140 students in an examination of a certain paper:

Marks:	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Number of students :	20	24	40	36	20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

Solution

18. The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f₁ and f₂ .

Class:	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120
Frequency:	5	F1	10	F2	7	8

Solution

19. The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find out the missing frequency.

Class interval:	11 – 13	13 – 15	15 – 17	17 – 19	19 – 21	21 – 23	23 – 25
Frequency:	7	6	9	13	-	5	4

Solution

20. If the mean of the following distribution is 27, find the value of p.

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency:	8	P	12	13	10

Solution

21. In a retail market, fruit vendors were selling mangoes kep in packing boxes. These boxes contained varying number of mangoes. The following was the distribuion of mangoes according to the number of boxes.

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

Solution

22. The table below shows the daily expenditure on food of 25 household in a locality.

Daily expenditure(in Rs):	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.

Solution

23. 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 fo 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.

Solution

24. 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

Solution

We may find class mark of each interval by using the relation 
So, mean number of days is 12, 38 days for which student was absent. 

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

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

Solution