Question

workers a and b, doing the same job, show the following results over a long period, what are the coefficients of variations of workers a & b?
worker | a | b
mean time of completing job (in hours) | 5 | 4
standard deviation (in hours) | 1.5 | 1.5
a = 32% & b= 38.2%
a = 25% & b= 40%
a = 30% & b= 37.5%
a = 28% & b= 32.2%

Explanation:

Step1: Recall Coefficient of Variation Formula

The formula for the coefficient of variation (CV) is \( CV = \frac{\text{Standard Deviation (SD)}}{\text{Mean}} \times 100\% \).

Step2: Calculate CV for Worker A

For Worker A, Mean (\(\mu_A\)) = 5 hours, SD (\(\sigma_A\)) = 1.5 hours.
Using the formula: \( CV_A = \frac{1.5}{5} \times 100\% \)
\( CV_A = 0.3 \times 100\% = 30\% \).

Step3: Calculate CV for Worker B

For Worker B, Mean (\(\mu_B\)) = 4 hours, SD (\(\sigma_B\)) = 1.5 hours.
Using the formula: \( CV_B = \frac{1.5}{4} \times 100\% \)
\( CV_B = 0.375 \times 100\% = 37.5\% \).

Answer:

A = 30% & B= 37.5%