box plot

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

## Definitions

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 = |q75 – q25| (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 than lowerInnerFence
  upperWhisker = largest data value smaller than upperInnerFence

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

  • the horizontal lines of the rectangle correspond to q25, q50 and q75, respectively.
  • the dotted line corresponds to the mean.
  • the outliers outside the outerFences are drawn with an 'o'.
  • the outliers in the intervals (lowerOuterFence, lowerInnerFence) and (upperInnerFence, upperOuterFence) are drawn with an '*'.
  • the whisker lines outside the rectangle connect q25 with lowerWhisker, and, q75 with upperWhisker, respectively. With no outliers present, the whiskers mark minimum and/or maximum of the data.

### Links to this page

- Table: Box plots...
- TableOfReal: Draw box plots...