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. The coefficient of variation for the waiting times at Bank A isThe coefficient of variation for the waiting times at Bank B is(Round to one decimal place as needed.)

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

Bank A (single line):

6.5 6.6 6.6 6.7 7.0 7.2 7.5 7.6 7.7 7.7

Bank B (individual lines):

4.1 5.5 5.8 6.2 6.7 7.7 7.7 8.5 9.3 9.9

Step 02:

coefficient of variation:

$CV\text{ = }\frac{standard\text{ deviation}}{mean}\text{ * 100\%}$

Bank A (single line):

$mean\text{ = 7.1}$$standard\text{ deviation = }\sqrt{\frac{2.169}{10}}=0.47$$cv\text{ =}\frac{0.47}{7.1}*100\text{ \% = 6.62 \%}$

cva = 6.6 %

Bank B (individual lines):

$mean\text{ = 7.14}$$standard\text{ deviation = }\sqrt{\frac{29.564}{10}}=1.72$

$cv\text{ = }\frac{1.72}{7.14}*100\text{ \% = 24.08 \%}$

cvb = 24.1 %

Comparison:

cvb > cba

That is the full solution.