- Interquartile range
descriptive statistics, the interquartile range (IQR), also called the midspread, middle fifty and middle of the #s, is a measure of statistical dispersion, being equal to the difference between the third and first quartiles.
Unlike the (total) range, the interquartile range is a
robust statistic, having a breakdown pointof 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.
For a symmetric distribution (so the median equals the
midhinge, the average of the first and third quartiles), half the IQR equals the median absolute deviation(MAD).
medianis the corresponding measure of central tendency.
Data setin a table:
From this table, the width of the interquartile range is 115 − 105 = 10.
Data set in a plain-text
+-----+-+ o * |-------| | |---
+-----+-+ +---+---+---+---+---+---+---+---+---+---+---+---+ number line 0 1 2 3 4 5 6 7 8 9 10 11 12
* lower (first) quartile (, ) = 7
* median (second quartile) (, ) = 8.5
* upper (third) quartile (, ) = 9
* interquartile range,
Interquartile range of distributions
The interquartile range of a continuous distribution can be calculated by integrating the
probability density function(which yields the cumulative distribution function—any means of calculating the CDF will also work). The lower quartile, a, is the integral of the PDF from -∞ to a that equals 0.25, while the upper quartile, b, is the integral from "b" to ∞ that equals 0.25; in terms of the CDF, the values that yield 0.25 and 0.75 are the quartiles.
[insert equations here]
The interquartile range and median of some common distributions are shown below
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Look at other dictionaries:
interquartile range — statistical measure of the spread of values around the median. When the upper, or higher, 25% of values and the lower 25% of values are removed, the spread of the remaining, interquartile, values is derived … Geography glossary
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