WOLFRAM|DEMONSTRATIONS PROJECT

Chebyshev's Inequality

number of standard deviations k

zoom

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

1001-

1

2

k

%

of the data elements will lie within

k

standard deviations of the mean, where

k>1

. That is, at least

1001-

1

2

k

%

of the data will lie between

μ-kσ

and

μ+kσ

for

k>1

, where

μ

is the mean and

σ

is the standard deviation of the distribution. This Demonstration illustrates the minimal percentage of data elements found within

k

standard deviations of any dataset's mean.