RD Sharma Solutions Chapter 7 Statistics Exercise 7.5 Class 10 Maths
Chapter Name  RD Sharma Chapter 7 Statistics 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 7.5 Solutions
1. Find the mode of the following data:
(i) 3,5,7,4,5,3,5,6,8,9,5,3,5,3,6,9,7,4
(ii) 3,3,7,4,5,3,5,6,8,9,5,3,5,3,6,9,7,4
(iii) 15,8,26,25,24,15,18,20,24,15,19,15
Solution
2. The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows:
Shirt size: 
37 
38 
39 
40 
41 
42 
43 
44 
Number of persons: 
15 
25 
39 
41 
36 
17 
15 
12 
Find the model shirt size worn by the group.
Solution
Shirt size:  37  38  39  40  41  42  43  44 
Frequency (f)  15  25  39  41  36  17  15  12 
Model shirt size = 40 because it occurs maximum number of times
(i)
Class interval: 
0 – 10 
10 – 20 
20 – 30 
30 – 40 
40 – 50 
50 – 60 
60 – 70 
70 – 80 
Frequency: 
5 
8 
7 
12 
28 
20 
10 
10 
(ii)
Class – inteval: 
10 – 15 
15 – 20 
20 – 25 
25 – 30 
30 – 35 
35 – 40 
Frequency: 
30 
45 
75 
35 
25 
15 
(iii)
Class – interval: 
25 – 30 
30 – 35 
35 – 40 
40 – 45 
45 – 50 
50 – 60 
Frequency: 
25 
34 
50 
42 
38 
14 
Solution
Age(in years): 
16 – 18 
18 – 20 
20 – 22 
22 – 24 
24 – 26 
Group A 
50 
78 
46 
28 
23 
Group B 
54 
89 
40 
25 
17 
Solution
= 18.83
Hence the mode of age for the group A is higher than group B.
Marks: 
0 – 10 
10 – 20 
20 – 30 
30 – 40 
40 – 50 
50 – 60 
60 – 70 
70 – 80 
80 – 90 
90 – 100 
Frequency: 
3 
5 
16 
12 
13 
20 
5 
4 
1 
1 
Solution
Height(in cm): 
160 – 162 
163 – 165 
166 – 168 
169 – 171 
172 – 174 
No. of students: 
15 
118 
142 
127 
18 
Find the average height of maximum number of students.
Solution
Age(in years): 
5 – 15 
15 – 25 
25 – 35 
35 – 45 
45 – 55 
55 65 
No. of students: 
6 
11 
21 
23 
14 
5 
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Solution
8. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
Lifetimes (in hours): 
0 – 20 
20 – 40 
40 – 60 
60 – 80 
80 – 100 
100 – 120 
No. of components: 
10 
35 
52 
61 
38 
29 
Determine the modal lifetimes of the components.
Solution
From data as given above we may observe that maximum class frequency 61 belonging to
class interval 60  80.
So, modal class 60  80
9. The following data gives the distribution of total monthly houshold expenditure of 200 families of a village. Find the modal monthly expenditure of the families.Also, find the mean monthly expenditure:
Expenditure (in Rs.) 
Frequency 
Expenditure(in Rs.) 
Frequency 
1000 – 1500 
24 
3000 – 3500 
30 
1500 – 2000 
40 
3500 – 4000 
22 
2000 – 2500 
33 
4000 – 4500 
16 
2500 – 3000 
28 
4500 – 5000 
7 
Solution
Number of students per teacher 
Number of states/U.T. 
Number of students per teacher 
Number of states/U.T. 
15 – 20 
3 
35 – 40 
3 
20 – 25 
8 
40 – 45 
0 
25 – 30 
9 
45 – 50 
0 
30 – 35 
10 
50 – 55 
2 
Solution
Runs scored 
No. of batsman 
Runs scored 
No. of batsman 
3000 – 4000 
4 
7000 – 8000 
6 
4000 – 5000 
18 
8000 – 9000 
3 
5000 – 6000 
9 
9000 – 10000 
1 
6000 – 7000 
7 
10000 – 11000 
1 
Find the mode of the data.
Solution
From the given data we may observe that maximum class frequently is 18 belonging to
class interval 4000  5000
So modal class 4000  5000
Lower limit(1) of model class = 4000
12. A student noted the number of cars passing through a spot on a road for loo periods each of 3 minutes and summarized it in the table given below. Find the mode of the data:
Solution
From the given data we may observe that maximum class internal frequency is 200 belonging to modal class = 40  50
13. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data the compare them.
Monthly consumption(in units) 
65 – 85 
85 – 105 
105 – 125 
125 – 145 
145 – 165 
165 – 185 
185 – 205 
No. of consumers: 
4 
5 
13 
20 
14 
8 
4 
Solution
Number of letters: 
1 – 4 
4 – 7 
7 – 10 
10 – 13 
13 – 16 
16 – 19 
Number surnames: 
6 
30 
40 
16 
4 
4 
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.
Solution
Classes: 
0 – 20 
20 – 40 
40 – 60 
60 – 80 
80 – 100 
100 – 120 
120 – 140 
Frequency: 
6 
8 
10 
12 
6 
5 
3 
Solution
Classes : 
0 – 50 
50 – 100 
100 – 150 
150 – 200 
200 – 250 
250 – 300 
300 – 350 
Frequency: 
2 
3 
5 
6 
5 
3 
1 
Solution
Daily income(in Rs) 
100 – 120 
120 – 140 
140 – 160 
160 – 180 
180 – 200 
Number of workers: 
12 
14 
8 
6 
10 
Find the mean, mode and median of the above data.
Solution