Collect the data values in a list.
Choose the type of standard deviation:
Population standard deviation (use when data is the entire population)
Sample standard deviation (use when data is a sample)
Compute the mean:
( mu = frac{1}{N}sum_{i=1}^{N} x_i ) (population)
( bar{x} = frac{1}{n}sum_{i=1}^{n} x_i ) (sample)
Compute each deviation from the mean:
( x_i – mu ) or ( x_i – bar{x} )
Square each deviation:
( (x_i – mu)^2 ) or ( (x_i – bar{x})^2 )
Sum the squared deviations:
( sum_{i=1}^{N} (x_i – mu)^2 ) or ( sum_{i=1}^{n} (x_i – bar{x})^2 )
Divide by the correct denominator:
Population: ( frac{1}{N}sum_{i=1}^{N} (x_i – mu)^2 )
Sample: ( frac{1}{n-1}sum_{i=1}^{n} (x_i – bar{x})^2 )
Take the square root to get standard deviation:
Population: ( sigma = sqrt{frac{1}{N}sum_{i=1}^{N} (x_i – mu)^2} )
Sample: ( s = sqrt{frac{1}{n-1}sum_{i=1}^{n} (x_i – bar{x})^2} )
If using a calculator/spreadsheet:
Population: Excel/Google Sheets `STDEV.P(range)`
Sample: Excel/Google Sheets `STDEV.S(range)`