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Definitions of Symmetric and Skewed
Having ways of looking at the center
of a batch of data values and the
spread of those data values allows us to ask the important question of whether
the spread is the same on both sides of the center. We want to know whether
the data values are bunched up on one side of the center and stretched out
on the other side or whether the spread is the same on both sides. Histograms
and box plots provide a visual means for assessing the similarity of the spread
on both sides of the center.
Symmetric
If the data are spread out the same on both sides of the center, then the
data are symmetric.
In both the histogram and the box plot below, you can see that the data have
the same spread on either side and that the shape on either side of the median
is the same.
Skewed
If the data are spread out differently on both sides of the center, then
the data are skewed.
A symmetric histogram could be folded at the center and both sides would
match. This is clearly not the case in the histogram below where the data values
are bunched at the low end and stretched out at the high end. In the box plot,
the median does not fall in the middle of the box and the whiskers are different
lengths--both indicators of skew.
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© 1999, Duxbury Press.
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