Question

14.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)	Bank B (individual lines)
6.4	4.3
6.5	5.5
6.6	5.9
6.8	6.3
7.1	6.7
7.4	7.6
7.4	7.8
7.7	8.4
7.7	9.4
7.8	9.7

The coefficient of variation for the waiting times at Bank A is ____%.

​(Round to one decimal place as​ needed.)

The coefficient of variation for the waiting times at the Bank B is ____.

​(Round to one decimal place as​ needed.)

Is there a difference in variation between the two data​ sets?

A.There is no significant difference in the variations.

B.The waiting times at Bank B have considerably less variation than the waiting times at Bank A.

c.The waiting times at Bank A have considerably less variation than the waiting times at Bank B.

Answer 1

For bank A

Mean = (6.4 + 6.5 + 6.6 + 6.8 + 7.1 + 7.4 + 7.4 + 7.7 + 7.7 + 7.8)/10
= 71.4/10
Mean = 7.14

The sample standard deviation is calculared as

Standard Deviation σ = √(1/10 - 1) x ((6.4 - 7.14)² + .................+ ( 7.8 - 7.14)²)
= √(1/9) x ((-0.74)² + ......................+ (0.66)²)
= √(0.1111) x ((0.5476) +................ + (0.4356))
= √(0.1111) x (2.564)
= √(0.2848604)
= 0.5337

and

=7.5%

For bank B

Mean = (4.3 + 5.5 + 5.9 + 6.3 + 6.7 + 7.6 + 7.8 + 8.4 + 9.4 + 9.7)/10
= 71.6/10
Mean = 7.16

Standard Deviation σ = √(1/10 - 1) x ((4.3 - 7.16)² + .......... + ( 9.7 - 7.16)²)
= √(1/9) x ((-2.86)² + (-1.66)² + (-1.26)² + ...........+ (2.24)² + (2.54)²)
= √(0.1111) x ((8.1796) + ..........+ (6.4516))
= √(0.1111) x (27.084)
= √(3.0090324)
= 1.7347

and

CV=24.2%

Hence,

c.The waiting times at Bank A have considerably less variation than the waiting times at Bank B.