stddev / var condensers

[Dimitar Misev]

SQL and various array DBMS support standard deviation and variance aggregations. Quoting from the SQL standard:

• If VAR_POP is specified, then the population variance of <value expression> evaluated for each row that qualifies, defined as the sum of squares of the difference of <value expression> from the mean of <value expression>, divided by the number of rows that qualify.
• If VAR_SAMP is specified, then the sample variance of <value expression> evaluated for each row that qualifies, defined as the sum of squares of the difference of <value expression> from the mean of <value expression>, divided by the number of rows that qualify minus 1 (one).
• If STDDEV_POP is specified, then the population standard deviation of <value expression> evaluated for each row that qualifies, defined as the square root of the population variance.
• If STDDEV_SAMP is specified, then the sample standard deviation of <value expression> evaluated for each row that qualifies, defined as the square root of the sample variance.