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Chebyshev's Inequality

number of standard deviations k

zoom

For any dataset, regardless of the shape of the distribution, at least

1001-

of the data elements will lie within

standard deviations of the mean, where

k>1

. That is, at least

1001-

of the data will lie between

μ-kσ

and

μ+kσ

for

k>1

, 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.

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