In descriptive statistics, the interquartile range (IQR), also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles, IQR = Q3 − Q1. In other words, the IQR is the 1st Quartile subtracted from the 3rd Quartile; these quartiles can be clearly seen on a box plot on the data. It is a trimmed estimator, defined as the 25% trimmed mid-range, and is the most significant basic robust measure of scale.
Data set in a table
i | x[i] | Quartile |
---|---|---|
1 | 102 | |
2 | 104 | |
3 | 105 | Q_{1} |
4 | 107 | |
5 | 108 | |
6 | 109 | Q_{2} (median) |
7 | 110 | |
8 | 112 | |
9 | 115 | Q_{3} |
10 | 116 | |
11 | 118 |
For the data in this table the interquartile range is IQR = 115 − 105 = 10.
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