InterQuartile Range (IQR) Calculator

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 (median)
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