Quartiles:
Quartiles:
If a data set of values is arranged in ascending order of magnitude, then:
• The median is the middle value of the data set.
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• The lower quartile (Q1) is the median of the lower half of the data set.
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• The upper quartile (Q3) is the median of the upper half of the data set.
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• The interquartile range (IQR) is the spread of the middle 50% of the data values. So:
The interquartile range is a more useful measure of spread than the range as it describes the middle 50% of the data values
Example
Find the median, lower quartile, upper quartile and interquartile range of the following data set of scores:
18 20 23 20 23 27 24 23 29
Solution:
Arrange the values in ascending order of magnitude:
18 20 20 23 23 23 24 27 29
There are 9 values in the data set.
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This means the middle 50% of the data values range from 20 to 25.5.
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