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Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal N(0,σ 2) Population. In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [1] The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread.
Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, [1] is a single-step multiple comparison procedure and statistical test.
where is the interquartile range of the data and is the number of observations in the sample . In fact if the normal density is used the factor 2 in front comes out to be ∼ 2.59 {\displaystyle \sim 2.59} , [ 4 ] but 2 is the factor recommended by Freedman and Diaconis.
The 4-quantiles are called quartiles → Q; the difference between upper and lower quartiles is also called the interquartile range, midspread or middle fifty → IQR = Q 3 − Q 1. The 5-quantiles are called quintiles or pentiles → QU; The 6-quantiles are called sextiles → S; The 7-quantiles are called septiles → SP; The 8-quantiles are ...
Simple L-estimators can be visually estimated from a box plot, and include interquartile range, midhinge, range, mid-range, and trimean. In statistics, an L-estimator (or L-statistic) is an estimator which is a linear combination of order statistics of the measurements. This can be as little as a single point, as in the median (of an odd number ...
The Interquartile Range (IQR), defined as the difference between the upper and lower quartiles (), may be used to characterize the data when there may be extremities that skew the data; the interquartile range is a relatively robust statistic (also sometimes called "resistance") compared to the range and standard deviation. There is also a ...
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Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.