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:

1. Order the data from least to greatest
2. Find the median
3. Construct a list of the lower half of the data (not including the median if the data set is odd)
4. Find the median of this lower half. This is the first quartile, Q1.
5. Construct a list of the upper half of the data (not including the median if the data set is odd)
6. Find the median of this upper half. This is the third quartile, Q3.
7. 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

• Quartile
• Median
• Range (statistics)
• Box plot
• Outlier

Interquartile range Resources
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