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 = 30% & b= 37.5%
a = 28% & b= 32.2%
a = 25% & b= 40%

Explanation:

Step1: Recall the formula for coefficient of variation (CV)

The formula for coefficient of variation 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: \( CV_A=\frac{\sigma_A}{\mu_A}\times 100\%=\frac{1.5}{5}\times 100\% \)
\( \frac{1.5}{5}=0.3 \), so \( CV_A = 0.3\times 100\% = 30\% \)

Step3: Calculate CV for Worker B

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

Answer:

A = 30% & B= 37.5%