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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.
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 ...
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. In order for these statistics to exist, the observations must be from a univariate variable that can be measured on an ordinal, interval or ratio scale .
The outliers would greatly change the estimate of location if the arithmetic average were to be used as a summary statistic of location. The problem is that the arithmetic mean is very sensitive to the inclusion of any outliers; in statistical terminology, the arithmetic mean is not robust.
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.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
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 ...
Another possible method to make the RMSD a more useful comparison measure is to divide the RMSD by the interquartile range (IQR). When dividing the RMSD with the IQR the normalized value gets less sensitive for extreme values in the target variable.