Interquartile range

[2][3][4] To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation.

The IQR is used to build box plots, simple graphical representations of a probability distribution.

[1] The quartile deviation or semi-interquartile range is defined as half the IQR.

[7] The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q3 and Q1.

For the data set in this box plot: This means the 1.5*IQR whiskers can be uneven in lengths.

The median, minimum, maximum, and the first and third quartile constitute the Five-number summary.

scores at 0.67 and −0.67 and not be normally distributed (so the above test would produce a false positive).

Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal N(0,σ 2 ) Population
Box-and-whisker plot with four mild outliers and one extreme outlier. In this chart, outliers are defined as mild above Q3 + 1.5 IQR and extreme above Q3 + 3 IQR.