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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.
Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.
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.
One of the most common robust measures of scale is the interquartile range (IQR), the difference between the 75th percentile and the 25th percentile of a sample; this is the 25% trimmed range, an example of an L-estimator. Other trimmed ranges, such as the interdecile range (10% trimmed range) can also be used.
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 ...
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 ...
In statistics, the interdecile range is the difference between the first and the ninth deciles (10% and 90%). The interdecile range is a measure of statistical dispersion of the values in a set of data, similar to the range and the interquartile range , and can be computed from the (non-parametric) seven-number summary .
Figure A: Line graph example. ... The maximum and minimum values are represented by the lines, and the interquartile range (IQR) represent 25–75% of the data.