Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3

Question 1.

From the data given below, state which group is more variable A or B?

Solution:

âˆ´ Ïƒ = 15.09.

Coefficient of variance (C.V.)

For Gropu B:

âˆ´ Ïƒ = 19.86

Coefficient of variance (C.V.)

= \(\frac{Ïƒ}{x}\) Ã— 100 = \(\frac{19.86}{44.6}\) Ã— 100 = 44.53.

Coefficient of variation in group B is greater than the coefficient of variation in group A. Therefore, group B is more variable than group A.

Question 2.

From the prices of shares X and Y below, find out which is more stable in value:

Solution:

For shares X:

For shares Y:

Coefficient of variation in shares Y is less than the coefficient of variation in shares X.

Therefore, the share Y is more stable than the share X.

Question 3.

An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, give the following results:

(i) Which firm A or B pays out larger amount of monthly wages?

(ii) Which firm A or B, shows greater variability in individual wages?

Solution:

For firm A:

No. of wage earners = 586.

Mean of monthly wages \(\bar {x}\) = â‚¹ 5253.

Amount paid by firm A = â‚¹ (586 Ã— 5253)

= â‚¹ 3078258.

Variance of distribution of wages = 100.

âˆ´ Standard deviation = Ïƒ = \(\sqrt{Variance}\) = \(\sqrt{100}\)

= 10.

âˆ´ Coefficient of variation = \(\frac{Ïƒ}{x}\) Ã— 100

= \(\frac{10}{5253}\) Ã— 100 = 0.19.

For firm B:

Number of wage earners = 648.

Mean of monthly wages \(\bar {x}\) = â‚¹ 5253.

Amount paid by firm B = â‚¹ 648 Ã— 5253.

= â‚¹ 3403944.

âˆ´ S.D. = Ïƒ = \(\sqrt{Variance}\) = \(\sqrt{121}\)

= 11.

âˆ´ Coefficient of variation = \(\frac{Ïƒ}{x}\) Ã— 100

= \(\frac{11}{5253}\) Ã— 100 = 0.21

Monthly wages paid by firm A = â‚¹ 3078258.

Monthly wages paid by firm B = â‚¹ 3403944.

Firm B pays out larger amount as monthly wages.

Coefficient of vanation of wages of firm A = 0.19.

Coefficient of vanation of wages of firm B = 0.21.

Therefore, firm B shows greater variability in individual wages.

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 standard deviation 1.25 goals. Find which team may be considered more consistent?

Solution:

For Team A:

âˆ´ Coefficient of variation

= \(\frac{Ïƒ}{x}\) Ã— 100 = \(\frac{1.095}{2}\) Ã— 100

= 54.75

For Team B:

Mean \(\bar {x} \) = 2

and S.D. = Ïƒ = 1.25.

Coefficient of variation

= \(\frac{Ïƒ}{x}\) Ã— 100 = \(\frac{1.25}{2}\) Ã— 100

= 62.5.

Coefficient of variation of goals of team A is less than that of B. Therefore, team A is more consistent than team B.

Question 5.

The sum and sum of squares corresponding to length x (in cm) and weight y (in grams) of 50 plant products are given below:

\(\sum_{i=1}^{50}\)x_{i} = 212, \(\sum_{i=1}^{50}\)x_{i}^{2} = 902.8, \(\sum_{i=1}^{50}\)y_{i} = 261, \(\sum_{i=1}^{50}\)y_{i}^{2} = 1457.6.

Which is more varying, the length or weight?

Solution:

For Length:

Coefficient of variation

= \(\frac{Ïƒ}{x}\) Ã— 100 = \(\frac{0.28}{4.24}\) Ã— 100 = 6.6

For weight:

Coefficient of variation of weight is more than that of length.

âˆ´ Weight is more varying than length.