vdoc

214 Part IV: Quality Assurance
25% 25% 25%
Quartiles Q 1 Q 2
Q 3
25%
Percentiles 25th 50th 75th
Figure 18.7 Quartiles and percentiles.
quartiles are sometimes also known as the lower, middle, and upper quartiles
respectively. Also note that the second quartile is the same as the median. To
determine the values of the different quartiles, one just has to find the 25th, 50th,
and 75th percentiles (see Figure 18.7).
Interquartile Range
Often we are more interested in finding information about the middle 50 percent of
a population. A measure of dispersion relative to the middle 50 percent of the population
or sample data is known as the interquartile range. This range is obtained by
trimming 25 percent of the values from the bottom and 25 percent from the top.
Interquartile range (IQR) is defined as
IQR = Q 3 – Q 1 (18.12)
Notes:
1. The interquartile range gives the range of variation among the middle 50
percent of the population.
Part IV.A.3
EXAMPLE 18.14
Find the interquartile range for the salary data in example 18.13:
Salaries: 48, 51, 51, 52, 54, 55, 58, 62, 63, 69, 72, 73, 76, 85, 95
Solution:
In order to find the interquartile range we need to find the quartiles Q 1 and Q 3 or equivalently
the 25th percentile and the 75th percentile. We can easily see that the ranks of
25th and 75th percentiles are:
Rank of 25th percentile = 25/100(15 + 1) = 4
Rank of 75th percentile = 75/100(15 + 1) = 12
Thus, in this case, Q 1 = 52 and Q 3 = 73.
This means that the middle 50 percent of the engineers earn between $52,000 and
$73,000. The interquartile range in this example is
IQR = $73,000 – $52,000 = $21,000