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): 6.5 6.6 6.7 6.9 7.1 7.3 7.4 7.6 7.7 7.8
Bank B (individual lines): 4.4 5.4 5.7 6.2 6.7 7.7 7.8 8.4 9.4 9.9

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. The waiting times at Bank B have considerably less variation than the waiting times at Bank A
B. There is no significant difference in the variations.
C. The waiting times at Bank A have considerably less variation than the waiting times at Bank B

Answer 1

Mean of Bank A

= ( 6.5 + 6.6 + 6.7 + 6.9 + 7.1 + 7.3 + 7.4 + 7.6 + 7.7 + 7.8 ) / 10

= 71.6 / 10

= 7.16

Standard deviation of Bank A

= sqrt [ ( 6.5 - 7.16 ) ^ 2 + ( 6.6 - 7.16 ) ^ 2 + ( 6.7 - 7.16 ) ^ 2 + ( 6.9 - 7.16 ) ^ 2 + ( 7.1 - 7.16 ) ^ 2 + ( 7.3 - 7.16 ) ^ 2 + ( 7.4 - 7.16 ) ^ 2 + ( 7.6 - 7.16 ) ^ 2 + ( 7.7 - 7.16 ) ^ 2 + ( 7.8 - 7.16 ) ^ 2 ] / 10

= sqrt ( 0.2004 )

= 0.4477

Coefficient of variation of Bank A

= 0.4477 / 7.16 * 100

= 6.2528 ~ 6.3

= 6.3 % ( Rounded to one decimal place )

Mean of Bank B

= ( 4.4 + 5.4 + 5.7 + 6.2 + 6.7 + 7.7 + 7.8 + 8.4 + 9.4 + 9.9 ) / 10

= 71.6 / 10

= 7.16

Standard deviation of Bank B

= sqrt [ ( 4.4 - 7.16 ) ^ 2 + ( 5.4 - 7.16 ) ^ 2 + ( 5.7 - 7.16 ) ^ 2 + ( 6.2 - 7.16 ) ^ 2 + ( 6.7 - 7.16 ) ^ 2 + ( 7.7 - 7.16 ) ^ 2 + ( 7.8 - 7.16 ) ^ 2 + ( 8.4 - 7.16 ) ^ 2 + ( 9.4 - 7.16 ) ^ 2 + ( 9.9 - 7.16 ) ^ 2 ] / 10

= sqrt ( 2.8744 )

= 1.6954

Coefficient of variation of Bank B

= 1.6954 / 7.16 * 100

= 23.6788 ~ 23.7

= 23.7 % ( Rounded to one decimal place )

Hence Yes ,There is a difference in variation between the two data sets .

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

i.e., ( 6.3 % is less than 23.7 % )

The Correct option is ( C ) .