InterQuartile Range (IQR) Calculator

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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 Q1
4 107
5 108
6 109 Q2
7 110
8 112
9 115 Q3
10 116
11 118

For the data in this table the interquartile range is IQR = 115 − 105 = 10.

Boxplot (with an interquartile range) and a probability density function of a Normal N(0,σ2) Population provides you helpful and handy calculator resources.