**Next:** Standard deviation **Up:** Single Variable Summary statistics **Previous:** Percentiles

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Box plots - also known as quantile plots

The box plot is a graphic which display the center portions of the data and
some information about the range of the data. There are a number of variations.

**The Five Number Summary Box Plot.**

This is a common variant and is drawn by first finding the minimum and
maximum values and the 25^{th}, 50^{th}, and 75^{th} percentiles
.

Then the box plot (either horizontal or vertical) as drawn as shown below:

**Variations on the box-plot** Sometimes the whiskers on the
box-plot have a different methods of constructions, however, the hinges are are
always computed as the 25^{th}, 50^{th}, and 75^{th}
percentiles.

- outliers may be identified using an outlier detection rule and are
displayed using asterisks or some other character.
- whiskers extend to 10
^{th} and 90^{th} percentiles;
- whiskers also identify other percentiles; see JMP help on quantile plots

We will make a slight detour here to examine JMP-IN's two types of box-plots
and show how to use the help feature to findout what they mean.

**Important** The actual computation of a box-plot is not that important
(that is what computers are used for), but understanding what box-plots show and
how to use them is important (what computer can't do!).

**Interpreting the box plot**

- central box includes the middle 50% of the data
- whiskers show range of data
- symmetry is indicated by box and whiskers and by location of the mean
- it is easy to compare groups by constructing side-by-side box plots as
shown below.

**Example of side-by-side box-plot** Here
is boxplot of births in a hospital in Canada by day of the week. What patterns
do you see? What unusual features are present?

**Next:** Standard deviation **Up:** Single Variable Summary statistics **Previous:** Percentiles
Copyright 1998: Carl J. Schwarz cschwarz@cs.sfu.ca