What is the 1 5 IQR rule

Box whiskers plot

The Box whisker plot (also Box plot or in German Box graphic is a common type of diagram that comprises five parameters (minimum, maximum, 1st quartile, median and 3rd quartile). The name comes from English and refers to the appearance of the diagram.

Box whisker plots show differences between populations without making assumptions about the underlying distribution function. All characteristic values ​​that are shown belong to thenonparametric statistics. This means that no assumptions are made about the underlying distribution function.

Readable parameters

The readable characteristic values ​​include the directly readable characteristic values:

  • lower quartile (1st quartile)
  • Median (2nd quartile)
  • upper quartile (3rd quartile)
  • minimum
  • maximum

In addition, other properties of the data can be read from the appearance of the diagram:


The skewness of the distribution function can be determined from the position of the median within the box. If the median is exactly in the middle of the box, then is the underlying distribution function symmetrical. However, if the median is on the left, then the data is left part (or poorly wrong). On the other hand, if the median is closer to the right, then the data is right part (or left skew). This information only applies to unimodal distribution functions.


The whiskers are not always drawn in with the box whisker plot. In this case the diagrams are simply called box plots. However, in the reverse case, the term box plot does not necessarily mean that the diagram has no whiskers.

Even if the whiskers mostly indicate the minimum or maximum of the data, this is not uniformly regulated. In some box whisker plots, the whiskers relate to the interquartile range. Since the interquartile range (IQR) is also used to Runaway to determine, data points that have been classified as outliers are usually plotted after or in front of the whiskers in such a box whisker plot. Most of the time, outliers are shown as asterisks (*), and in specific studies you can often see the specific number of the data set written next to it. The whiskers are then usually at 3rd quartile + 1.5 (IQR) for the maximum and 1st quartile - 1.5 (IQR) for the minimum.

With this convention, however, one would normally assume that both whiskers are the same length because they are each 1.5 times the median. However, by convention, the last data point that lies within the interquartile range is usually taken as the point where the whisker ends.