Editing Standard deviation (section)

===Chebyshev's inequality===
{{main|Chebyshev's inequality}}
An observation is rarely more than a few standard deviations away from the mean. Chebyshev's inequality ensures that, for all distributions for which the standard deviation is defined, the amount of data within a number of standard deviations of the mean is at least as much as given in the following table.

{|class="wikitable"
|-
! Distance from mean !! Minimum population
|-
| <math>\sqrt{2}\,\sigma</math> || 50%
|-
| <math>2\sigma</math> || 75%
|-
| <math>3\sigma</math> || 89%
|-
| <math>4\sigma</math> || 94%
|-
| <math>5\sigma</math> || 96%
|-
| <math>6\sigma</math> || 97%
|-
| <math>k\sigma</math> || <math>1 - \frac{1}{k^2}</math><ref>{{cite book|last=Ghahramani|first=Saeed|year=2000|title=Fundamentals of Probability|url=https://archive.org/details/fundamentalsprob00ghah_271|url-access=limited|edition=2nd|publisher=Prentice Hall|location=New Jersey|page=[https://archive.org/details/fundamentalsprob00ghah_271/page/n445 438]|isbn=9780130113290 }}</ref>
|-
| <math>\frac{1}{\sqrt{1 - \ell}}\, \sigma</math> || <math>\ell</math>
|}