# Formulas for Variance and Standard Deviation by variablepitch346

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```									Formulas for Variance and Standard Deviation In all formulae n =
Population (or Sample if interested in Sample Parameters only) Mean

f
Sample Statistics



 fx
n

x
 fx
n
2

 fx
n

Variance



2

 f (x  )
n

2

=


2

2

sn

2

 f ( x  x)
n

2

=

 fx
n

2

x

2

Standard Deviation


S
2 n-1

 f (x  )
n

2

=

 fx
n

 2

sn

 f ( x  x)
n

2

=

 fx
n

2

x

2

Unbiased Estimate of Population Variance

 n  S n-1 =    n 1 
2

sn

2

=

 f ( x  x)
n 1

2

=

 fx

2

n 1



n 2 x n 1

The Casio gives the following statistics: n, x,  x,  x 2 , xσn which is the standard deviation of the data put into the calculator (our

σ or sn

above) , and xσn-1 which is the unbiased estimate of the population standard deviation (our sn-1 above). The Texas gives σn for the population standard deviation and sn for the unbiased estimate of the population standard deviation.

```
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