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