Box Plot

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Box Plot - short version

Graph commonly used to display differences between categorical x's.

Box Plot - long version

A box plot or boxplot (also known as a box-and-whisker diagram or plot) is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation (sample minimum), lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation (sample maximum). A boxplot may also indicate which observations, if any, might be considered outliers.

Boxplots display differences between populations without making any assumptions of the underlying statistical distribution: they are non-parametric. The spacings between the different parts of the box help indicate the degree of dispersion (spread) and skewness in the data, and identify outliers. Boxplots can be drawn either horizontally or vertically.

Box and whisker plots are uniform in their use of the box: the bottom and top of the box are always the 25th and 75th percentile (the lower and upper quartiles, respectively), and the band near the middle of the box is always the 50th percentile (the median). But the ends of the whiskers can represent several possible alternative values, among them:

* the minimum and maximum of all the data

* the lowest datum still within 1.5 IQR of the lower quartile, and the highest datum still within 1.5 IQR of the upper quartile

* one standard deviation above and below the mean of the data

* the 9th percentile and the 91st percentile

* the 2nd percentile and the 98th percentile.

Any data not included between the whiskers should be plotted as an outlier with a dot, small circle, or star, but occasionally this is not done. Some box plots include an additional character to represent the mean of the data. On some box plots a crosshatch is placed on each whisker, before the end of the whisker. Rarely, box plots can be presented with no whiskers at all. Because of this variability, it is appropriate to describe the convention being used for the whiskers and outliers in the caption for the plot. The unusual percentiles 2%, 9%, 91%, 98% are sometimes used for whisker cross-hatches and whisker ends to show the seven-number summary. If the data are normally distributed the locations of the seven marks on the box plot will be equally spaced.