Gujarat Board Textbook Solutions Class 11 Statistics Chapter 4 Measures of Dispersion Ex 4.5

Gujarat Board Statistics Class 11 GSEB Solutions Chapter 4 Measures of Dispersion Ex 4.5 Textbook Exercise Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Statistics Chapter 4 Measures of Dispersion Ex 4.5

Question 1.
Price fluctuations of two shares A and B are given below, which type of share has more relative variation in its price?

Answer:
To determine which share price has more relative variation, we calculate coefficient of variation of prices of share A and share B.

Share A
Mean:
x̄ = $\frac{\Sigma x}{n}=\frac{3210}{10}$ = ₹ 321

Standard deviation:
s = $\sqrt{\frac{\Sigma(x-\bar{x})^{2}}{n}}$
= $\sqrt{\frac{70}{10}}$
= √7
= ₹ 2.65

Coefficient of variation:
Variation = $\frac{s}{\bar{x}}$ × 100
= $\frac{2.65}{321}$ × 100
= 0.0083 × 100
= 0.83%

Share B
Mean:
x̄ = $\frac{\Sigma x}{n}=\frac{1400}{10}$ = ₹ 140

Standard deviation:
s = $\sqrt{\frac{\Sigma(x-\bar{x})^{2}}{n}}$
= $\sqrt{\frac{510}{10}}$
= √51
= ₹ 7.14

Coefficient of variation:
Variation = $\frac{s}{\bar{x}}$ × 100
= $\frac{7.14}{140}$ × 100
= 0.051 × 100
= 5.1%

Coefficient of variation of price of share A 0.83% and that of share B it is 5.1%. Hence, the relative measure of variation is more in the price of share B.

Question 2.
The daily salary of administrative staff of two companies yielded the following results:

	Company A	Company B
Mean salary(₹)	600	2100
Standard Deviation (₹)	30	84

Which company has more stable salary?
Answer:
Company A
x̄ = ₹ 600
s = ₹ 30

Coefficient of variation = $\frac{s}{\bar{x}}$ × 100
= $\frac{30}{600}$ × 100
= 5%

Company B:
x̄ = ₹ 2100
s = ₹ 84

Coefficient of variation = $\frac{s}{\bar{x}}$ × 100
= $\frac{84}{2100}$ × 100
= 4%

The coefficient of variation of daily salary of employees of company A is 5 % and that of company B it is 4 %. Hence, the daily salary in company B Is more stable.

Question 3.
The Coefficients of variation of two series are 30% and 25% and their standard deviations are 15 and 9 respectIvely. Find their means.
Answer:
First Series:
Coefficient of variation: 30%
s = 15
x̄ = ?

Coefficient of variation = $\frac{s}{\bar{x}}$ × 100
∴ 30 = $\frac{15}{\bar{x}}$ × 100
∴ 30x̄ = 1500
∴ x̄ = $\frac{1500}{30}$
∴x̄ = 50

Second series:
Coefficient of variation: 25%
s = 9
x̄ = ?

Coefficient of variation = $\frac{s}{\bar{x}}$ × 100
∴ 25 = $\frac{9}{\bar{x}}$ × 100
∴ 25x̄ = 900
∴ x̄ = $\frac{900}{25}$
∴x̄ = 36