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Concept
Interquartile range
Summary
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‐spread. It is defined as the difference between the 75th and 25th percentiles of the data. To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q1 (also called the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 − Q1.
The IQR is an example of a trimmed estimator, defined as the 25% trimmed range, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. It is also used as a robust measure of scale It can be clearly visualized by the box on a box plot.
Unlike total range, the interquartile range has a breakdown point of 25%, and is thus often preferred to the total range.
The IQR is used to build box plots, simple graphical representations of a probability distribution.
The IQR is used in businesses as a marker for their income rates.
For a symmetric distribution (where the median equals the midhinge, the average of the first and third quartiles), half the IQR equals the median absolute deviation (MAD).
The median is the corresponding measure of central tendency.
The IQR can be used to identify outliers (see below). The IQR also may indicate the skewness of the dataset.
The quartile deviation or semi-interquartile range is defined as half the IQR.
The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q3 and Q1. Each quartile is a median calculated as follows.
Given an even 2n or odd 2n+1 number of values
first quartile Q1 = median of the n smallest values
third quartile Q3 = median of the n largest values
The second quartile Q2 is the same as the ordinary median.
Official source
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