Interquartile range
Interquartile range (IQR) is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles, Q3 and Q1. The IQR is the first quartile subtracted from the third quartile; these quartiles can be clearly seen on a box plot on the data.
Definition
The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the values lie, the interquartile range is a measure of where the central values lie. The IQR is used in statistics to identify outliers.
Calculation
To calculate the interquartile range:
- Order the data from least to greatest
- Find the median
- Construct a list of the lower half of the data (not including the median if the data set is odd)
- Find the median of this lower half. This is the first quartile, Q1.
- Construct a list of the upper half of the data (not including the median if the data set is odd)
- Find the median of this upper half. This is the third quartile, Q3.
- Subtract Q1 from Q3 to find the interquartile range.
Applications
The interquartile range is often used in conjunction with other statistical tools, such as the box plot, to provide a graphical representation of statistical dispersion in a set of data. It is also used in statistical analysis to identify and manage outliers, as it is less sensitive to extreme values than other measures of dispersion.
See also
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Contributors: Prab R. Tumpati, MD
