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Standard Deviation

Author: Katherine Williams

Calculating Standard Deviation

Source: Image of Graph Creative Commons Graph: http://wikimediafoundation.org/wiki/File:6_Sigma_Normal_distribution.jpg

Video Transcript
Terms to Know
Standard Deviation

A typical amount by which we would expect a data point to differ from the mean. Typically, about half to two-thirds of the data points fall within one standard deviation of the mean.

Variance

The square of standard deviation. While it has some uses in statistics, it is not a practical unit of measurement. It is calculated the same way as standard deviation, but without the square root.

Formulas to Know
Standard Deviation of a Sample

s equals square root of fraction numerator 1 over denominator n minus 1 end fraction sum from i equals 1 to n of open parentheses X subscript i minus X with bar on top close parentheses squared end root

n equals n u m b e r space o f space d a t a space p o i n t s
X subscript i equals e a c h space o f space t h e space v a l u e s space i n space t h e space d a t a space s e t
X with bar on top equals m e a n space o f space t h e space d a t a space s e t

Variance of a Sample

s squared equals fraction numerator 1 over denominator n minus 1 end fraction sum from i equals 1 to n of left parenthesis X subscript i minus X with bar on top right parenthesis squared