## Modified Boxplots

Move the "seed" slider to select a new set of data.

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A modified boxplot is a boxplot with values below the
lower fence and values above the upper fence removed
and marked as possible outliers. Here possible outliers
are marked with an "x".

The lower fence is at x = Q1 - 1.5 * IQR.

The upper fence is at x = Q3 + I.5 * IQR.

The IQR is the interquartile range: IQR = Q3 - Q1.
Since the IQR is the length of the box in the boxplot,
outliers are data that is more than 1.5 boxlengths
from the boxplot box.

Q1 is the lower quartile, which separates the
smallest 25% of data values from the largest 75%.
The vertical line in the boxes is the median, which
separates the smallest 50% of the data values
from the largest 50% of the data values.
Q3 is the upper quartile, which separates the
smallest 75% of data values from the largest 25%.

The only purpose of the fences is to determine
which if any values are possible outliers. The
fences are not a necessary part of the graph and
can be removed by unchecking the check box.

If there are outliers on the lower end, the minimum
of the non-outlying or reasonable data is chosen
as the new minimum. Similarly, if there are outliers
on the upper end, the maximum of the non-outlying
or reasonable data is chosen as the new maximum.

David Gurney, Created with GeoGebra