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Chapter 18: A. Basic Statistics and Applications 213
EXAMPLE 18.13
The following data give the salaries (in thousands of dollars) of 15 engineers of a
corporation:
62, 48, 52, 63, 85, 51, 95, 76, 72, 51, 69, 73, 58, 55, 54
Find the 70th percentile for these data.
Solution:
Write the data values in ascending order and rank them from 1 to 15, since n is equal
to 15.
Step 1. Salaries: 48, 51, 51, 52, 54, 55, 58, 62, 63, 69, 72, 73, 76, 85, 95
Rank: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Step 2. Find the rank of the 70th percentile, which is given by 70 ×
((15 + 1)/100) = 11.2
Step 3. Find the data value that corresponds to the rank 11.2, which will
be the 70th percentile. From Figure 18.6, we can easily see that the
value of the 70th percentile is given by:
70th percentile = 72(.8) + 73(.2) = 72.2
Thus, the 70th percentile of the salary data is $72,200.
That is, at the most 70 percent of the engineers are making less than $72,200 and at the
most 30 percent of the engineers are making more than $72,200.
11 11.2
72
.2 .8
Figure 18.6 Salary data.
12
73
Part IV.A.3
For instance, in Example 18.13 the percentile corresponding to the salary of
$60,000 is
P = 7/(15 + 1)100 = 44.
Thus, the engineer who makes a salary of $60,000 is at the 44th percentile. In other
words, at most 44 percent of the engineers are making less than $60,000 or at most
56 percent are making more than $60,000.
Quartiles
In the previous discussion we studied the percentiles, which divide the data into
100 equal parts. Some of the percentiles have special importance. These important
percentiles are the 25th, 50th, and 75th percentiles and are known as the
first, second, and third quartiles (denoted by Q 1 , Q 2 , and Q 3 ) respectively. These