box plot

A box plot provides a simple graphical summary of data. These plots originate from the work of Tukey (1977).


The following figure shows an annotated box plot.

To understand the box plot we need the following definitions:

q25 = lower quartile, 25% of the data lie below this value
q50 = median, 50% of the data lie below this value
q75 = upper quartile, 25% of the data lie above this value

The following definitions all depend on these quantiles:

hspread = |q75q25| (50% interval)
lowerOuterFence = q25 – 3.0 * hspread (not in figure)
lowerInnerFence = q25 – 1.5 * hspread (not in figure)
upperInnerFence = q75 + 1.5 * hspread
upperOuterFence = q75 + 3.0 * hspread
lowerWhisker = smallest data value larger then lowerInnerFence
upperWhisker = largest data value smaller then upperInnerFence

The box plot is a summary of the data in which:

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© djmw, October 10, 2011