Question

I'm very confused as to finding out percentiles, quartiles and deciles - I've looked at formulas but am not exactly sure how they translate. Any help would be appreciated!

Exercise 14:

Kevin Horn is the national sales manager for National Textbooks, Inc. He has a sales staff of

40 who visit & bribe 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

bribed during the previous week. Listed below, ordered from smallest to largest, are the

number of visits last week. 22 40 41 41 48 48 50 50 51 51 52 52 53 54 55 55 55 56 24 57 59 59 59 62 62 62 63 64 65 77 66 67 67 69 69 71 28 78 79 90 a. Find the median 56.5 b. Find the first quartile c. Find the ninth decile d. Find the thirty-third percentile

Answer 1

Solution:

First of all we have to arrange the given data in an increasing order. (You can also arrange the given data in a decreasing order.)

X	Order
22	1
24	2
28	3
40	4
41	5
41	6
48	7
48	8
50	9
50	10
51	11
51	12
52	13
52	14
53	15
54	16
55	17
55	18
55	19
56	20
57	21
59	22
59	23
59	24
62	25
62	26
62	27
63	28
64	29
65	30
66	31
67	32
67	33
69	34
69	35
71	36
77	37
78	38
79	39
90	40

Part a

Median = Middle most observation when data is in an increasing (or decreasing) order

Total number of observations = n = 40

n is even

So, middle observations are 20^th observation and 21^st observation

Median = average of the 20^th observation and 21^st observation

20^th observation = 56

21^st observation = 57

Median = (56 + 57) / 2 = 56.5

Median = 56.5

Part b

First quartile is the (1/4)*40 = 0.25*40 = 10^th observation

First quartile = 50

Part c

Ninth decile is the (9/10)*40 = 0.9*40 = 36^th observation

Ninth decile = 71

Part d

Thirty third percentile is the (33/100)*40 = 0.33*40 = 13.2 ≈ 13^th observation

Thirty third percentile = 52