# Standard Deviation Calculator

Standard deviation (SD) measured the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ). The following algorithmic calculation tool makes it easy to quickly discover the mean, variance & SD of a data set.

## Math Formulas

**Mean** = sum of values / N (number of values in set)

**Variance** = ((n_{1}- Mean)^{2} + ... n_{n}- Mean)^{2}) / N-1 (number of values in set - 1)

**Standard Deviation** σ = √Variance

**Population Standard Deviation **= use N in the Variance denominator if you have the full data set. The reason 1 is subtracted from standard variance measures in the earlier formula is to widen the range to "correct" for the fact you are using only an incomplete sample of a broader data set.

### Example Calculation

for data set 1,8,-4,9,6 compute the *SD* and the *population SD*.

**Sum:** 1+8+-4+9+6=20

**Mean:** 20/5 numbers = mean of 4

**Variance:** ((1-4)^{2} + (8-4)^{2} + (-4-4)^{2} + (9-4)^{2} + (6-4)^{2}) / (N-1) =

((-3)^{2} +( 4)^{2} + (-8)^{2} + (5)^{2} + (2)^{2} ) / 4 =

(9+16+64+25+4)/4 =

118/4 = 29.5

**Standard Deviation:** √29.5= 5.43139

**Population Standard Deviation Variance:** 118 / N = 118 / 5 = 23.6

**Population Standard Deviation:** √23.6= 4.85798

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