MEASURES of SPREAD
(Quartiles and Percentiles)
Quartiles divide a set of ORDERED data into
four groups with equal numbers of values.
The three dividing points are:
1. the first quartile, Q1
2. the median or second quartile, Q2
3. the third quartile, Q3
Interquartile Range

Lowest Datum
n 1


 4 

First Quartile
Q1
th

Median
Q2
n 1


 2 
position

Third Quartile
Q3
th

Highest Datum
th
position
 3(n  1) 

 position
 4 
The interquartile range is defined as Q3 – Q1, which is the range of the
middle half of the data. This range provides a measure of spread by
showing how closely the data are clustered around the median.
The semi-interquartile range is one half of the interquartile range.
A box-and-whisker plot illustrates Q1, Q2, and Q3. The box is defined by
each quartile and shows the interquartile range while the ends of the
“whiskers” represent the lowest and highest values in the data.
Interquartile Range
Lowest Value
Q1
Q2
(median)
Q3
Highest Value
Example 
Determine the indicated quantities for each of the following sets:
a) 18, 15, 20, 17, 11, 9, 13, 14, 17, 16, 10, 16
n=
Rank Data:
Quartile
median (Q2)
Position
Value
n 1

2
Q1
n 1

4
Q3
3(n  1)

4
Q3 – Q1
(interquartile range)
semi-interquartile range
b) 4, 5, 8, 7, 3, 1, 2, 5, 3
n=
Rank Data:
Quartile
median (Q2)
Position
Value
n 1

2
Q1
n 1

4
Q3
3(n  1)

4
Illustrate with a box-and-whisker plot.

1

2

3

4

5

6

7

8
MEASURES of SPREAD
(Percentiles)
Percentiles divide the ordered data into 100
intervals that have equal numbers of values.
35% of data is less than
or equal to this value
eg. 35th percentile, P35
65% of data is greater than
or equal to this value
Example 
35
38
41
44
45
45
An audio magazine tested 60 different models of
speakers and gave each one an overall rating based on
sound quality, reliability, efficiency, and appearance.
The raw scores for the speakers are listed in ascending
order below.
47
50
51
53
53
56
57
58
58
59
60
62
62
62
62
63
63
64
64
65
65
66
67
67
67
68
68
69
69
70
72
72
73
74
75
75
76
78
79
81
82
82
83
84
86
86
87
88
Determine each of the following:
a)
P35
b)
P20
c)
Determine the percentile corresponding to a score of 79.
90
91
92
94
96
98