Suspected outlier(s):
Suspected outliers
appear in a boxplot as individual points o
or x outside the box. The o outlier values are known
as outside values, and the x outlier values as
far outside values.
If the difference (distance) between
the 75th and 25th percentiles of the data is H,
then the outside values are those values that are
more than 1.5H but no more than 3H above the upper quartile,
and those values that are
more than 1.5H but no more than 3H below the lower quartile.
The far outside values are values that are at least
3H above the upper quartile or 3H below the lower quartile.
If there are only a few outliers,
and the boxplot otherwise has the mean (+) value
close to the median (the center line in the box)
and the median line evenly divides the box, then
there may be anomalous data values in a
sample
that otherwise
comes from a normal
or near-normal distribution.
If there are numerous outliers
to one side or the other of the box,
or the median line does not evenly divide the box, then
the population
distribution from which the data were sampled may be
skewed.
If there are numerous outliers on both sides of the box,
the population distribution from which the data were sampled may be
heavy-tailed.
Here is an example of a boxplot with a possible outlier
at the lower range of the data:
Skewness to the right:
If the boxplot shows outliers at the upper range of the data
(above the box), the mean (+) value is above the
median (the center line in the box), the median line does not
evenly divide the box, and the upper tail
of the boxplot is longer than the lower tail,
then the population distribution
from which the data were
sampled
may be
skewed
to the right.
Here is a hypothetical example of a boxplot for
data sampled from a distribution
that is skewed to the right:
The distribution
from which the data were sampled may be both
skewed
to the right and
heavy-tailed,
in which case there may be outliers on both sides of
the box, but predominantly above the box.
Skewness to the left:
If the boxplot shows outliers at the lower range of the data
(below the box), the mean (+) value is below the
median (the center line in the box), the median line does not evenly divide the box,
and the lower tail of the boxplot is longer than the upper tail,
then the population distribution
from which the data were
sampled
may be
skewed to the left.
Here is a hypothetical example of a boxplot for
data sampled from a distribution
that is skewed to the left:
The distribution from which the data were sampled may be both
skewed
to the left and
heavy-tailed,
in which case there may be outliers on both sides of
the box, but predominantly below the box.
Light-tailedness:
Data sampled
from a
light-taileddistribution
produce a boxplot with no outliers,
and with the tails of the box short relative to
the height of the box. Light-tailedness may be hard to detect from a boxplot.
Here is a hypothetical example of a boxplot for
data sampled from a light-tailed distribution:
The distribution from which the data were sampled may be both
skewed
to the right and
light-tailed,
in which case the mean (+) value is above the
median (the center line in the box),
the median line does not evenly divide the box,
and the upper tail
of the boxplot is longer than the lower tail.
The distribution from which the data were sampled may be both
skewed
to the left and
light-tailed,
in which case the mean (+) value is below the
median (the center line in the box),
the median line does not evenly divide the box,
and the lower tail
of the boxplot is longer than the upper tail.
Heavy-tailedness:
Data
sampled
from a
heavy-taileddistribution
produce a boxplot with outliers on
both sides of the box, and with the tails of the box long relative to
the height of the box.
Here is a hypothetical example of a boxplot for
data sampled from a heavy-tailed distribution:
The distribution from which the data were sampled may be both
skewed
to the right and
heavy-tailed,
in which case there may be outliers on both sides of
the box, but predominantly above the box, the
mean (+) value is above the median (the center line in the box),
and the median line does not evenly divide the box.
The distribution from which the data were sampled may be both
skewed
to the left and
heavy-tailed,
in which case there may be outliers on both sides of
the box, but predominantly below the box, and the
mean (+) value is below the median (the center line in the box),
and the median line does not evenly divide the box.
Mixtures of normal distributions:
Data may be
sampled
from a mixture of
normal distributions.
Depending on the means and variances of the component normal
distributions, and on the relative proportions of the data
that come from each distribution, a mixture of normal distributions
may produce a variety of boxplots.
Here is a hypothetical example of a boxplot for
data sampled from a mixture of two normals with the
same mean but different variances:
Such a mixture of normal distributions may be hard to distinguish
from a symmetric, heavy-tailed
distribution.
Here is a hypothetical example of a boxplot for
data sampled from a mixture of two normals with the
same variance but different means:
Such a mixture of normal distributions may be hard to distinguish
from a light-tailed distribution.
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