Standard deviation

Standard deviation measures the variation of values about their mean. The sample standard deviation is the square root of the sample variance.

The sample variance uses Bessel's correction, dividing the sum of squared deviations from the sample mean by n - 1 rather than n. This gives an unbiased estimator of the population variance under standard sampling assumptions. The standard deviation of an analysis domain is calculated as follows:

The summation is over all included samples i in the analysis domain.

n	is the number of samples included in the summation.
Ei	is the linear Sv of sample i (m2/m3) -  set to 0 for any sample where Ei < mSv or Ei > MSv,
En	is the observed Mean Energy of the analysis domain in linear units (m2/m3) = 10Sv/10
mSv	is the minimum integration threshold (dB re 1 m-1) at time of processing.
MSv	is the maximum integration threshold (dB re 1 m-1) at time of processing.
ESD	is the Standard deviation.

For Linear data, Ei is the sample value and En is the arithmetic mean of the included sample values in the analysis domain.

For Linear, TS, Power dB, and Unspecified dB data, standard deviation returns no data when fewer than two samples are included.

For information about undefined calculations for these data types, see the Standard deviation, Skewness and Kurtosis note.

All symbols are as defined in the nomenclature developed for SHAPES algorithms.

See also

About Standard deviation
School Detection module algorithms
Other region variables for schools analysis