QUARTILES & INTERQUARTILE RANGES
Quartiles: Divide a set of ordered data into four groups with equal numbers of values, just as the
median divides data into two equally sized groups.
 There are three 'dividing points'
◦ 1st Quartile, Q1
◦ Median or 2nd Quartile, Q2
◦ 3rd Quartile, Q3
 Q1 and Q3 are the medians of the lower and upper halves of the data
Recall: When there are an even number of data points, you take the midpoint between the two middle
values as the median (Q2)
 If the number of data below the median is even, Q1 is the midpoint between the two
middle values in this half, similarly, Q3 would be the midpoint in the upper half
Interquartile Range: Q3 – Q1, the range of the middle half of the data
 The larger the spread of the central half of the data, the larger the interquartile range
 The interquartile range provides the measure of spread
Semi-Interquartile Range: It is one half of the interquartile range.
 Both of these ranges indicate how closely the data are clustered around the median
Box-and-whisker plot: This illustrates these measures of spread.
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The box shows Q1, the median, and Q3
The ends of the 'whiskers' represent the lowest and highest values in the set of data
The length of the box shows the interquartile range
The left whisker shows the range of the data below Q1
The right whisker shows the range of the data above Q3
Modified Box-and-whisker plot: This is used when there are outliers in the data.
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Typically, any point that is at least 1.5 times the box length away from the box is
classified as an outlier.
The outliers are shown as separate points instead of including them in the whiskers
Example: A random survey of people at a science-fiction convention asked them how many times
they had seen Star Wars. The results are shown below.
3
4
2
8
10
5
1
15
5
16
6
3
4
9
12
3
30
2
10
7
a) Determine the median, the first and third quartiles, and the interquartile and semi-interquartile
ranges. What information do these measures provide?
b) Prepare a suitable box plot of the data.
c) Compare the results in part a) to those from last year’s survey, which found a median of 5.1
with an interquartile range of 7.0.
Example: In a survey of low risk mutual funds, the median annual yield was 7.2%, while Q1 was
5.9% and Q3 was 8.3%. Describe the following funds in terms of quartiles.
Mutual Fund
XXY Value
YYZ Dividend
ZZZ Bond
Annual Yield (%)
7.5
9.0
7.2