Class 11 Maths NCERT Solutions for Chapter 15 Statistics Exercise 15.3
Statistics Exercise 15.3 Solutions
1. From the data given below state which group is more variable, A or B?
Marks 
1020 
2030 
3040 
4050 
5060 
6070 
7080 
Group A 
9 
17 
32 
33 
40 
10 
9 
Group B 
10 
20 
30 
25 
43 
15 
7 
Marks 
Group A f_{i} 
Mid – point x_{i} 
y_{i}^{2} 
f_{i} y_{i} 
f_{i} y_{i}^{2} 

10 – 20 
9 
15 
3 
9 
27 
81 
20 – 30 
17 
25 
2 
4 
34 
68 
30 – 40 
32 
35 
1 
1 
32 
32 
40 – 50 
33 
45 
0 
0 
0 
0 
50 – 60 
40 
55 
1 
1 
40 
40 
60 – 70 
10 
65 
2 
4 
20 
40 
70 – 80 
9 
75 
3 
9 
27 
81 
150 
6 
342 
The standard deviation of group B is calculated as follows.
Marks 
Group A f_{i} 
Mid – point x_{i} 
y_{i}^{2} 
f_{i} y_{i} 
f_{i} y_{i}^{2} 

10 – 20 
10 
15 
3 
9 
30 
90 
20 – 30 
20 
25 
2 
4 
40 
80 
30 – 40 
30 
35 
1 
1 
30 
30 
40 – 50 
25 
45 
0 
0 
0 
0 
50 – 60 
43 
55 
1 
1 
43 
43 
60 – 70 
15 
65 
2 
4 
30 
60 
70 – 80 
7 
75 
3 
9 
21 
63 
150 
6 
366 
Since the mean of both the groups is same, the group with greater standard deviation will be more variable.
Thus, group B has more variability in the marks.
X 
35 
54 
52 
53 
56 
58 
52 
50 
51 
49 
Y 
108 
107 
105 
105 
106 
107 
104 
103 
104 
101 
35, 54, 52, 53, 56, 58, 52, 50, 51, 49
Here, the number of observations, N = 10
The following table is obtained corresponding to shares X.
x_{i} 

35 
16 
256 
54 
3 
9 
52 
1 
1 
53 
2 
4 
56 
5 
25 
58 
7 
49 
52 
1 
1 
50 
1 
1 
51 
0 
0 
49 
2 
4 
350 
The prices of share Y are
108, 107, 105, 105, 106, 107, 104, 103, 104, 101
The following table is obtained corresponding to shares Y.
y_{i} 


108 
3 
9 
107 
2 
4 
105 
0 
0 
105 
0 
0 
106 
1 
1 
107 
2 
4 
104 
1 
1 
103 
2 
4 
104 
1 
1 
101 
4 
16 
40 
C.V. of prices of shares X is greater than the C.V. of prices of shares y.
Firm A 
Firm B 

No. of wage earners 
586 
648 
Mean of monthly wages 
Rs 5253 
Rs 5253 
Variance of the distribution of wages 
100 
121 
(ii) Which firm, A or B, shows greater variability in individual wages?
(i) Monthly wages of firm A = Rs 5253
Number of wage earners in firm A = 586
∴Total amount paid = Rs 5253 × 586
Monthly wages of firm B = Rs 5253
Number of wage earners in firm B = 648
∴Total amount paid = Rs 5253 × 648
Thus, firm B pays the larger amount as monthly wages as the number of wage earners in firm B are more than the number of wage earners in firm A.
(ii) Variance of the distribution of wages in firm A (Ïƒ_{1}^{2}) = 100
∴ Standard deviation of the distribution of wages in firm
A ((Ïƒ_{1}) = √100 = 10
Variance of the distribution of wages in firm B (Ïƒ_{2}^{2}) = 121
∴ Standard deviation of the distribution of wages in firm B (Ïƒ_{2}^{2}) = √121 = 11
The mean of monthly wages of both the firms is same i.e., 5253. Therefore, the firm with greater
standard deviation will have more variability.
Thus, firm B has greater variability in the individual wages.
4. The following is the record of goals scored by team A in a football session:
No. of goals scored 
0 
1 
2 
3 
4 
No. of matches 
1 
9 
7 
5 
3 
No. of goals scored 
No. of matches 
f_{i} x_{i} 
x_{i}^{2} 
f_{i}x_{i}^{2} 
0 
1 
0 
0 
0 
1 
9 
9 
1 
9 
2 
7 
14 
4 
28 
3 
5 
15 
9 
45 
4 
3 
12 
16 
48 

25 
50 

130 
The standard deviation of team B is 1.25 goals.
The average number of goals scored by both the teams is same i.e., 2. Therefore, the team with lower standard deviation will be more consistent.
Thus, team A is more consistent than team B.
5. The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:
Which is more varying, the length or weight?
Solution
Thus, C.V. of weights is greater than the c.v. of lengths. Therefore, weights vary more than the lengths.