Math CentralQuandaries & Queries


Question from Paula, a teacher:

Is it possible for a box-and-whisker plot to have no whiskers? 3 whiskers?

Hi Paula,

For a box-and-whisker plot you order the data numerically from smallest to largest and find the lower quartile, median and upper quartile. The box extends from the lower quartile to the upper quartile and there is a whisker to the left of the lower quartile representing the data points that are less than the lower quartile, and a whisker to the right of the upper quartile representing the data points that are greater than the upper quartile. Thus there can't be three whiskers. But can there be no whiskers? Can there be no data points less than the lower quartile and no data points greater than the upper quartile?

The simplest example I can think of is a three element data set {1, 2, 3}. The median is 2, the lower quartile (the median of the values less than the median) is 1 and the upper quartile is 3. Thus the box extends from 1 to 3 are there are no whiskers.

You could construct a larger data set with the same property. You might have a thousand ones, a thousand twos and a thousand threes. Now the data set has three thousand elements but still no whiskers.

I hope this helps,

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