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 nbsp 6.7 nbsp 6.7 nbsp 6.8 nbsp 7.1 nbsp 7.3 nbsp 7.4 nbsp 7.7 nbsp 7.7 nbsp 7.7 Bank B​ (individual lines): 4.3 nbsp 5.4

Answer 1

Complete Question

1. 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 lines): 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7

Bank B (individual lines): 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7

- The coefficient of variation for the waiting times at Bank A is ----- %?

- The coefficient of variation for the waiting times at the Bank B is ----- ​%?

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

Answer:

a

The coefficient of variation for the waiting times at Bank A is
`l =`6.3%

b

The coefficient of variation for the waiting times at Bank B is
`l_1 =`25.116%

c

The waiting time of Bank B has a considerable higher variation than that of Bank A

Explanation:

From the question we are told that

For Bank A : 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7

For Bank B : 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7

The sample size is n =10

The mean for Bank A is

`\mu_A = (6.5+ 6.6+ 6.7+ 6.8+ 7.2+ 7.3+ 7.4+ 7.6+ 7.6+ 7.7)/(10)`

`\mu_A = 7.14`

The standard deviation is mathematically represented as

`\sigma = \sqrt(\sum`

`k = \sum |x- \mu | ^2 = 6.5 -7.14|^2 + |6.6-7.14|^2+ |6.7-7.14|^2+ |6.8-7.14|^2 + |7.2-7.14|^2+ |7.3-7.14|^2, |7.4-7.14|^2+ |7.6-7.14|^2+|7.6-7.14|^2+|7.7-7.14|^2`

`k = 2.42655`

`\sigma = \sqrt{(2.42655)/(10) }`

`\sigma = 0.493`

The coefficient of variation for the waiting times at Bank A is mathematically represented as

`l = (\sigma)/(\mu) *100`

`l = (0.493)/(7.14) *100`

`l =`6.3%

Considering Bank B

The mean for Bank B is

`\mu_1 = (4.1+ 5.4+ 5.8+ 6.3+6.8+ 7.8+ 7.8+ 8.6+ 9.3+ 9.7)/(10)`

`\mu_1 = 7.16`

The standard deviation is mathematically represented as

`\sigma_1 = \sqrt)/(n)`

`\sum |x- \mu_1 | ^2 =4.1-7.16|^2 +| 5.4-7.16|^2+ |5.8-7.16|^2 + | 6.3-7.16|^2 + |6.8-7.16|^2 + | 7.8-7.16|^2 +|7.8-7.16|^2 +|8.6-7.16|^2 + |9.3-7.16|^2 +|9.7-7.16|^2`

`\sum |x- \mu_1 | ^2 =32.34`

`\sigma_1 = \sqrt{(32.34)/(10) }`

`\sigma_1 = 1.7983`

The coefficient of variation for the waiting times at Bank B is mathematically represented as

`l_1 = (\sigma )/(\mu) *100`

`l_1 = (1.7983 )/(7.16) *100`

`l_1 =`25.116%