Question

Kevin Horn is the national sales manager for National Textbooks Inc. He has a sales staff of 40 who visit college professors all over the U.S. Each Saturday morning, he requires his sales staff to send him a report. This report includes, among other things, the number of professors visited during the previous week. Listed below, ordered from smallest to largest are the number of visits last week.

38, 40, 41, 45, 48, 48, 50, 50, 51, 51, 52, 52, 53, 54, 55, 55, 55, 56, 56, 57, 59, 59, 59, 62, 62, 62, 63, 64, 65,66, 66, 67, 67, 69, 69, 71, 77, 78, 79, 79
a. determine the median number of calls
b. determine the 1st and 3rd quartiles
c. determine the first decile and the ninth decile
d. determine the 33rd percentile

Answer 1

Following are the solution to the given points:

Explanation:

Given values:

`38, 40, 41, 45, 48, 48, 50, 50, 51, 51, 52, 52, 53, \\\\`
`54, 55, 55, 55, 56, 56, 57, 59, 59, 59, 62, 62, 62, \\ 63, 64, 65,66, 66, 67, 67, 69, 69, 71, 77, 78, 79, 79`

Total staff=40

In point a:

To calculate the median number first we arrange the value into ascending order and then collect the even numbers of calls that were also made. Its average of the middle terms is thus the median.

The midterms =55 and 59 so,

Median =
`(55+59)/(2) = (114)/(2)=57`

In point b:

First-quarter
`Q_1 = (1)/(4) \text{number of 8th call}`

`=(1)/(4) * 30 th \\\\= 7.5 th`

The first quarterlies are
`7.5th \ \ that \ is = (7+0.5)th\ \ term`

therefore the multiply of 0.5 by calculating the difference of the 7th and 8th term are:

`=0.5 * 0= 0 \\\\\to Q_1 = 50+0=50 \\\\\to Q_3=(3)/(4) \text{number of 8th call} \\\\=(3)/(4) * 30 th \\\\=22.5 \ th = (22+0.5)th \ \ term`

therefore the it is multiply by the 0.5 for the difference of the 22nd and 23rd term:

`= 0.5 * 1=0.5 \\\\\to Q_3= 63+0.5=63.5`

In point c:

First decile
`D_1 = (1)/(18) \text{number of 8th call}`

`= (1)/(10) * 30 th \\\\= 3rd \ \ term\\\\\to D_1= 41 \\\\\to D_9= (9)/(10) * 8\ th\ call\\\\=(9)/(10) * 30 th \\\\=27th \ \ term\\\\\to D9 = 67`

In point d:

quartiles are:

`Q_1= 51.25 \\\\Q_3=66`

The right answers for the decile are:

`D_1=45.3 \\\\ D_9=76.4`

As for
`D) P_(33) = 53.53`will be available.