Chebyshev's Inequality

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For any dataset, regardless of the shape of the distribution, at least of the data elements will lie within
standard deviations of the mean, where
. That is, at least
of the data will lie between
and
for
, where
is the mean and
is the standard deviation of the distribution. This Demonstration illustrates the minimal percentage of data elements found within
standard deviations of any dataset's mean.
Contributed by: Craig Bauling (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
M. Sullivan III, Statistics: Informed Decisions Using Data, New Jersey: Pearson, 2010.
Permanent Citation
"Chebyshev's Inequality"
http://demonstrations.wolfram.com/ChebyshevsInequality/
Wolfram Demonstrations Project
Published: March 7 2011