Question

Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below.

Find the coefficient of variation for each of the two sets of​ data, then compare the variation.

Bank A (single line): 6.6, 6.7, 6.7, 6.8, 7.0, 7.3, 7.5, 7.7, 7.8, 7.8Bank B (individual lines): 4.0, 5.5, 5.8, 6.2, 6.6, 7.6, 7.7, 8.5, 9.4, 9.7(Round to one decimal place as needed.)

Answer 1

CV of Bank A = 6.4

CV of Bank B = 7.1

CV of Bank B is more than CV of Bank A

Explanation:

Bank A

6.6, 6.7, 6.7, 6.8, 7.0, 7.3, 7.5, 7.7, 7.8, 7.8

`Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = (6.6+6.7+6.7+6.8+7.0+7.3+7.5+7.7+7.8+ 7.8)/(10)\\Mean =7.19`

Standard deviation =
`\sqrt{ \frac{\sum(x-\bar{x})^2}{n}}=0.461`

`CV = \frac{\sigma}{\bar{x}} * 100\\CV = (0.461)/(7.19) * 100=6.4`

Bank B

4.0, 5.5, 5.8, 6.2, 6.6, 7.6, 7.7, 8.5, 9.4, 9.7

`Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = (4.0+5.5+5.8+6.2+6.6+ 7.6+ 7.7+8.5+9.4+9.7)/(10)\\Mean =7.1`

Standard deviation =
`\sqrt{ \frac{\sum(x-\bar{x})^2}{n}}=1.718`

`CV = \frac{\sigma}{\bar{x}} * 100\\CV = (1.718)/(7.1) * 100=24.2`

CV of Bank A = 6.4

CV of Bank B = 7.1

CV of Bank B is more than CV of Bank A