Interquartile range

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In descriptive statistics, the interquartile range (IQR) is the difference between the third and first quartiles and is a measure of statistical dispersion. The interquartile range is a more stable statistic than the range, and is often preferred to that statistic.

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 should be measured in the same units as the data.

Interquartile range is used to build Box plots, that can give a simple graphical representation of a probability distribution.

[edit] Example

     i    x[i]
     1    102
     2    104
     3    105 ---- the first quartile, Q1 = 105 
     4    107
     5    108
     6    109 ---- the second quartile, Q2 or median = 109
     7    110
     8    112
     9    115 ---- the third quartile, Q3 = 115 
    10    115
    11    118

From this table, the interquartile range is 115 - 105 = 10.

The interquartile mean is a measure of central tendency.