# Interquartile range

The

**interquartile range** is the difference between the third and first quartiles (see

quartiles to learn about the first and third quartiles). Since 25% of the data are less than or equal to the first quartile and 25% are greater than or equal to the third quartile, the difference is the length of an interval that includes about half of the data. This difference is, of course, measured in the same units as the data. The interquartile range is more stable than the

statistical range and is usually preferred to that statistic.

We can illustrate the calculation using the same data we used for illustrating the quartiles.

i x[i]
1 102
2 105
----------- the first quartile, Q[1] = (105+106)/2 = 105.5
3 106
4 109
------------ the second quartile, Q[2] or median = 109.5
5 110
6 112
------------ the third quartile, Q[3] = (112+115)/2 = 113.5
7 115
8 118

From this table, you can see that the **interquartile range** is 113.5 - 105.5 = 8

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