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 6.8 7.0 7.2 7.3 7.7 7.7 7.7

Bank B​ (individual lines): 4.1 5.5 5.7 6.2 6.7 7.6 7.6 8.5 9.4 9.8

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

(Round to two decimal places as​ needed.)

The coefficient of variation for the waiting times at the Bank B is _​%.

​(Round to two decimal places 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

Answer:

$CV_A = \frac{0.471}{7.12}=0.07 = 7\%$

$CV_B = \frac{1.811}{7.11}=0.25 =25\%$

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

Step-by-step explanation:

The Coefficient of variation "shows the extent of variability in relation to the mean of the population" and is defined as:

$CV= \frac{\sigma}{\mu}$

And the best estimator is $\hat{CV} =\frac{s}{\bar X}$

Where the sample mean is obtained from:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation from:

$s=\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}$

Bank A

$\bar X_A =7.12$

$s_A=0.471$

$CV_A = \frac{0.471}{7.12}=0.07 = 7\%$

Bank B

$\bar X_B =7.11$

$s_B=1.811$

$CV_B = \frac{1.811}{7.11}=0.25 =25\%$

And the best option for this cas based on the results obtaines is:

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