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 United States. 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 first and third quartiles. (Round Q1 to 2 decimal places and Q3 to nearest whole number.)
c. Determine the first decile and the ninth decile. (Round your answer to 1 decimal place.)
d. Determine the 33rd percentile. (Round your answer to 2 decimal places.)

a. Median= 58

b. Q1 = 51.5‬

    Q3 = 66

c.  first decile= 45

    ninth decile= 76

d. 33rd percentile = 53

Step-by-step explanation:

a. To determine the median number of calls

Data from last week's visit are already arranged in order from smallest to largest. The median number of calls is the middle number in the ordered list:

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

Since the list total number is 40, the median would be the average of the 20th and 21st number.

Median= 57 + 59 / 2

            = 116 /2 = 58

b. To determine the first and third quartiles. (Round Q1 to 2 decimal places and Q3 to the nearest whole number.)

From: 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

After finding the median in the list, the first quartiles, Q1 is the median of the lower part of the list.

Q1 from 38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57

= The average of the 10th and 11th number

= 51 + 52 / 2 = 51.5‬

After finding the median in the list, the third quartiles, Q3 is the median of the upper part of the list.

Q3 from 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

= The average of the 10th and 11th number

= 66 + 66 / 2 = 66

c. To determine the first decile and the ninth decile. (Round your answer to 1 decimal place.)

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

Decile is used to divide data into smaller parts

Using the formula

Dm = m x ((n+1) / 10) th value

For the first decile,

D1 = 1 x ((40 + 1) / 10)

= 4.1

After this, We locate the fourth value in the ordered array and then have to move 0.1 of the distance between the fourth and the fifth values.

Using: 4th number + (5th number - 4th number) x 0.1

first decile= 45 + ( 48-45) x 0.1

  = 45.3

To nearest whole number = 45

For the ninth decile:

D9 = 9 x (( 40 + 1) /10)

= 36.9‬

After this, We locate the 36th value in the ordered array and then have to move 0.9 of the distance between the 36th and the 37th values.

ninth decile=  71 + ( 77 - 71) x 0.9

       = 76.4

To nearest whole number = 76

d. To determine the 33rd percentile. (Round your answer to 2 decimal places.)

33rd percentile from 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

using the formula n(p/100)

Where, n = sample size and p = percentile

= 40 (33/100)

= 13.2 ( round up to the nearest whole number)

= The 13th number in the list

33rd percentile = 53