Each of these functions takes a set of numbers, ignores nulls, and can be used as either an aggregate function or an analytic function.
The relationships among these functions are described in the following table:
| Function purpose | Function name | Formula | Comments |
|---|---|---|---|
| Population variance | VAR_POP(expr) | ( SUM(expr*expr) - SUM(expr)*SUM(expr) / COUNT(expr)) / COUNT(expr) | Applied to an empty set, it returns null. |
| Population standard deviation | STDDEV_POP(expr) | Square root of the population variance (VAR_POP). | When VAR_POP returns null, STDDEV_POP returns null. |
| Sample variance | VAR_SAMP(expr) | (SUM(expr*expr) - SUM(expr)*SUM(expr) / COUNT(expr)) / (COUNT(expr)−1) | Applied to an empty set, it returns null. Applied to an input set of one element, VAR_SAMP returns null. |
| Sample standard deviation | STDDEV_SAMP(expr) | Square root of the sample variance (VAR_SAMP). | Applied to only 1 row of input data, STDDEV_SAMP returns null. |
Returns the population variance of a non-null set of numbers (nulls being ignored).
VAR_POP uses the following calculation:
(SUM(expr*expr) - SUM(expr)\*SUM(expr) / COUNT(expr)) / COUNT(expr)
In other words, for a given set of non-null values, using S1 as the sum of the values and S2 as the sum of the squares of the values, VAR_POP returns the result (S2-S1*S1/N)/N.
You can use VAR_POP as either an aggregate and analytic function. Applied to an empty set, it returns null.
VAR_POP ( [DISTINCT | ALL] \<number-expression\> )
where ALL includes (and DISTINCT excludes) duplicate values in the input set. ALL is the default. When the the input set has no non-null data, VAR_POP returns NULL.
<number-expression> can be any any numeric expression.
Population Standard Deviation. Returns the returns the square root of the population variance (VAR_POP) for
STDDEV_POP ( [DISTINCT | ALL] \<number-expression\> )
where ALL includes (and DISTINCT excludes) duplicate values in the input set. ALL is the default. When the the input set has no non-null data, STDDEV_POP returns NULL.
<<number-expression>> can be any any numeric expression.
Returns the sample variance of a non-null set of numbers (nulls being ignored).
VAR_SAMP ( [DISTINCT | ALL] <number-expression> )
where ALL includes (and DISTINCT excludes) duplicate values in the input set. ALL is the default. When the the input set has no non-null data, VAR_SAMP returns NULL.
<number-expression> can be any any numeric expression.
VAR_SAMP uses the following calculation:
(SUM(expr*expr) - SUM(expr)\*SUM(expr) / COUNT(expr)) / (COUNT(expr)-1)
In other words, for a given set of non-null values, using S1 as the sum of the values and S2 as the sum of the squares of the values, VAR_POP returns the result (S2-S1*S1/N)/(N-1).
You can use VAR_SAMP as either an aggregate and analytic function. Applied to an empty set, it returns null. Given an input set of one element, VAR_SAMP returns null.
Returns the statistical standard deviation of all values in <number-expression>, evaluated for each row remaining in the group and defined as the square root of the [sample variance (VAR_SAMP)]#var_samp).
STDDEV_SAMP ( [DISTINCT | ALL] <\<number-expression\>> )
where ALL includes (and DISTINCT excludes) duplicate values in the input set. ALL is the default. When the the input set has no non-null data, STDDEV_SAMP returns NULL.
<number-expression> can be any any numeric expression.
STD_DEV is an alias of STDDEV_SAMP.