STDDEV: Calculating the Standard Deviation for a Set of Data Values

The STDDEV function returns a numeric value that represents the amount of dispersion in the data. The set of data can be specified as the entire population or a sample. The standard deviation is the square root of the variance, which is a measure of how observations deviate from their expected value (mean). If specified as a population, the divisor in the standard deviation calculation (also called degrees of freedom) will be the total number of data points, N. If specified as a sample, the divisor will be N-1.

If x¡ is an observation, N is the number of observations, and µ is the mean of all of the observations, the formula for calculating the standard deviation for a population is:

To calculate the standard deviation for a sample, the mean is calculated using the sample observations, and the divisor is N-1 instead of N.

Reference: Calculate the Standard Deviation in a Set of Data

STDDEV(field, sampling)

where:

field

Numeric

Is the set of observations for the standard deviation calculation.

sampling

Keyword

Indicates the origin of the data set. Can be one of the following values.

P Entire population.
S Sample of population.

Note: Arguments for STDDEV cannot be prefixed fields. If you need to work with fields that have a prefix operator applied, apply the prefix operators to the fields in COMPUTE commands and save the results in a HOLD file. Then, run the standard deviation against the HOLD file.

Example: Calculating a Standard Deviation

The following request calculates the standard deviation of the DOLLARS field converted to double precision.

DEFINE FILE ibisamp/ggsales
DOLLARS/D12.2 = DOLLARS;
END
TABLE FILE ibisamp/ggsales
SUM DOLLARS STDDEV(DOLLARS,S) 
ON TABLE SET PAGE NOLEAD
ON TABLE SET STYLE *
GRID=OFF,$
ENDSTYLE
END

The output is shown in the following image.