GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3

   

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?
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 1
Solution:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 2
∴ σ = 15.09.
Coefficient of variance (C.V.)

For Gropu B:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 3
∴ σ = 19.86
Coefficient of variance (C.V.)
= \(\frac{σ}{x}\) × 100 = \(\frac{19.86}{44.6}\) × 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.

GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3

Question 2.
From the prices of shares X and Y below, find out which is more stable in value:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 4
Solution:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 5
For shares X:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 6

For shares Y:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 7
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.

GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3

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:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 8
(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 \(\bar {x}\) = ₹ 5253.
Amount paid by firm A = ₹ (586 × 5253)
= ₹ 3078258.
Variance of distribution of wages = 100.
∴ Standard deviation = σ = \(\sqrt{Variance}\) = \(\sqrt{100}\)
= 10.
∴ Coefficient of variation = \(\frac{σ}{x}\) × 100
= \(\frac{10}{5253}\) × 100 = 0.19.

For firm B:
Number of wage earners = 648.
Mean of monthly wages \(\bar {x}\) = ₹ 5253.
Amount paid by firm B = ₹ 648 × 5253.
= ₹ 3403944.
∴ S.D. = σ = \(\sqrt{Variance}\) = \(\sqrt{121}\)
= 11.
∴ Coefficient of variation = \(\frac{σ}{x}\) × 100
= \(\frac{11}{5253}\) × 100 = 0.21
Monthly wages paid by firm A = ₹ 3078258.
Monthly wages paid by firm B = ₹ 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.

GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3

Question 4.
The following is the record of goals scored by team A in a football session:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 9
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:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 10

For Team A:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 11
∴ Coefficient of variation
= \(\frac{σ}{x}\) × 100 = \(\frac{1.095}{2}\) × 100
= 54.75

For Team B:
Mean \(\bar {x} \) = 2
and S.D. = σ = 1.25.
Coefficient of variation
= \(\frac{σ}{x}\) × 100 = \(\frac{1.25}{2}\) × 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.

GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3

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:
\(\sum_{i=1}^{50}\)xi = 212, \(\sum_{i=1}^{50}\)xi2 = 902.8, \(\sum_{i=1}^{50}\)yi = 261, \(\sum_{i=1}^{50}\)yi2 = 1457.6.
Which is more varying, the length or weight?
Solution:
For Length:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 12
Coefficient of variation
= \(\frac{σ}{x}\) × 100 = \(\frac{0.28}{4.24}\) × 100 = 6.6

For weight:
GSEB Solutions Class 11 Maths Chapter 15 Statistics Ex 15.3 img 13
Coefficient of variation of weight is more than that of length.
∴ Weight is more varying than length.

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