Factory A and Factory B employ 476 and 524 employees. respectively. The average weekly salary of an employee in Factory A is $34.5 whereas for an employee in Factory B it is $28.5, The standard deviation in paying the individual salary has been recorded as $5 and $4.5 for Factory A and Factory B, respectively. Which factory has greater variability in paying individual salary?

Given

Average weekly wages of factory A = 34.5

Average weekly wages of factory B = 28.5

Number of employees engaged in factory A = 476

Standard deviation (σ)_A = $5

Standard deviation (σ)_B = $4.5

Formula

For answering the question we have to find out the coefficient of variation

Coefficient of variation =( S.D. x 100 )/average wages

Calculation

coefficient of variation for factory A

⇒ ( 5.0 x 100 ) /34.5

⇒ 14.49

Coefficient of variation for factory B

⇒ ( 4.5 x 100 ) / 28.5
⇒ 15.78
Higher the coefficient of variation, the higher the variability of individual wages.

∴ Factory B is having higher variability in individual wages.

Standard deviation = Standard deviation is the square root of the mean of square of deviation from the arithmetic mean. The standard deviation is denoted by σ

σ = √[(1/n)∑(x_i – x̅)²]

If we square the standard devation we will get variance, therefore

Variance = σ² = [(1/n)∑(x_i – x̅)²]

For example

The standard deviation of 5, 10, 20 and 25 is

 Mean = (5 + 10 + 20 + 25)/4 = 15

SD = σ = √[(1/4)(5 – 15)² + (10 – 15)² + (20 – 15)² + (25 – 15)²]

σ = √[(1/4)(100 + 25 + 25 + 100)]

σ = √[(1/4)(250

σ = √125/2

Variance = σ² = 125/2

Coefficient of variation =  (Standard deviation/mean) × 100

(σ/x̅)× 100