# 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.

 Enter the numbers separated by comma ','E.g: 11,21,10,42,53 Total Numbers Mean (Average) SD Variance (SD) Population SD Variance(Population SD)

## Math Formulas

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

Variance = ((n1- Mean)2 + ... nn- 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