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If data are placed in order, then the lower quartile is central to the lower half of the data and the upper quartile is central to the upper half of the data. These quartiles are used to calculate the interquartile range, which helps to describe the spread of the data, and determine whether or not any data points are outliers.
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.
The quartile coefficient of dispersion is the ratio of half of the interquartile range (IQR) to the average of the quartiles (the midhinge): [1] = + = +. Example [ edit ]
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.
Robust measures of scale can be used as estimators of properties of the population, either for parameter estimation or as estimators of their own expected value.. For example, robust estimators of scale are used to estimate the population standard deviation, generally by multiplying by a scale factor to make it an unbiased consistent estimator; see scale parameter: estimation.
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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