Interquartile range

Interquartile range

In 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 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.

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).

The median is the corresponding measure of central tendency.


:"Example 1"

Data set in a table:

From this table, the width of the interquartile range is 115 − 105 = 10.

:"Example 2"

Data set in a plain-text box plot:

+-----+-+ o * |-------| | |---
+-----+-+ +---+---+---+---+---+---+---+---+---+---+---+---+ number line 0 1 2 3 4 5 6 7 8 9 10 11 12

For this data set:
* lower (first) quartile (Q1, x_{.25}) = 7
* median (second quartile) (Med, x_{.5}) = 8.5
* upper (third) quartile (Q3, x_{.75}) = 9
* interquartile range, mathrm{IQR} = Q3-Q1 = 2

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

ee also

* Midhinge

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См. также в других словарях:

  • 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

  • interquartile range — “+... noun Etymology: inter + quartile : the range of values of the variable in a statistical distribution that lies between the upper and lower quartiles * * * /in teuhr kwawr tuyl, til/, Statistics. the range of values of a frequency… …   Useful english dictionary

  • interquartile range — /in teuhr kwawr tuyl, til/, Statistics. the range of values of a frequency distribution between the first and third quartiles. [1880 85; INTER + QUARTILE] * * * …   Universalium

  • interquartile range — noun The difference between the first and third quartiles; a robust measure of sample dispersion. Syn: IQR, midspread …   Wiktionary

  • interquartile range — the difference between the data values at the 75th and 25th percentiles, encompassing the middle 50 per cent of the data …   Medical dictionary

  • Interquartile mean — The interquartile mean (IQM) is a statistical measure of central tendency, much like the mean (in more popular terms called the average), the median, and the mode. The IQM is a truncated mean and so is very similar to the scoring method used in… …   Wikipedia

  • Range (statistics) — In descriptive statistics, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observations from the greatest and provides an indication of statistical dispersion. It is… …   Wikipedia

  • Écart interquartile — En statistiques, l’écart interquartile[1] ou étendue interquartile[2] (EI) est une mesure de dispersion qui s obtient en faisant la différence entre le premier et le troisième quartiles : EI = Q3 Q1. L EI est un estimateur statistique… …   Wikipédia en Français

  • IQR — interquartile range …   Medical dictionary

  • IQR — • interquartile range …   Dictionary of medical acronyms & abbreviations

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