RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3

Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Textbook Exercise Questions and Answers.

RBSE Class 11 Maths Solutions Chapter 15 Statistics Ex 15.3

Question 1.
From the data given below state which group is more variable, A or B?
Answer:
Thus, variance of group B = 243.84
Clearly, Group B has more variation. Thus, group B is more variable.

Question 2.
From the prices of shares X and Y below, find out which is more stable in value?
Answer:
Clearly, variance of price of share Y is less.
Thus, there is more stability in share Y.

Question 3
An analysis of monthly wages paid to workers ¡n two firms A and B, belonging to the same Industry, gives them following results.

(i) Which firm A or B pays larger amount as monthly wages?
(ii) Which firm A or B shows greater variability In Individual wages?
Answer:
No. of workers got monthly wages by firm A = 586
Mean of wages of workers of firm A = 5,253
Thus, total wages of workers of firm A = 5,253 × 586 = ₹ 30,78,258
Variance of distribution of wages of firm A = σ² = 100
Thus, standard deviation of distribution of wages of
firm A = σ = √100 = 10
Then, coefficient of variable of wages of firm A (CV.)
= \(\frac{\sigma}{\bar{x}}\) × 100 = \(\frac{10}{5,253}\) × 100 = 0.19
Again, no. of workers got monthly wages by firm B = 648
Mean of wages of workers of firm B = ₹ 5,253
Thus, total wages of workers of firm B = 5,253 × 648 = ₹ 34,03,944
Variance of distribution of wages of firm B = σ² = 121
Thus, standard deviation of distribution of wages of firm B = σ = √121 = 11
Then, coefficient of variance of wages of firm B
(C.V.) = \(\frac{\sigma}{\bar{x}}\) × 100 = \(\frac{11}{5,253}\) × 100 = 0.21
Comparing wages of two firms A and B,
(i) Firm B pays larger amount as monthly wages
(ii) Firm B shows greater variability in individual wages (0.21 > 0.19).

Question 4.
The following is the record of goals scored by team A in a football session.

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?
Answer:
Table for computing coefficent of variation of team A

Clearly, coefficient of variation of team A is lesser as compared to team B.
Thus, team A is more consistent as compared to team B.

Question 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.

Answer: