# VARIANCE, VARIANCE_SAMP, VARIANCE_POP, VAR_SAMP, VAR_POP Functions

An aggregate function that returns the variance of a set of numbers. This is a mathematical property that signifies how far the values spread apart from the mean. The return value can be zero (if the input is a single value, or a set of identical values), or a positive number otherwise.

**Syntax:**

{ VARIANCE | VAR[IANCE]_SAMP | VAR[IANCE]_POP } ([DISTINCT | ALL]expression)

This function works with any numeric data type.

**Return type:** `DOUBLE` in Impala 2.0 and higher; `STRING` in earlier releases

This function is typically used in mathematical formulas related to probability distributions.

The `VARIANCE_SAMP()` and `VARIANCE_POP()` functions compute the sample variance and population variance, respectively, of the
input values. (`VARIANCE()` is an alias for `VARIANCE_SAMP()`.) Both functions evaluate all input rows matched by the query. The difference
is that `STDDEV_SAMP()` is scaled by `1/(N-1)` while `STDDEV_POP()` is scaled by `1/N`.

The functions `VAR_SAMP()` and `VAR_POP()` are the same as `VARIANCE_SAMP()` and `VARIANCE_POP()`, respectively. These aliases are available in Impala 2.0 and later.

If no input rows match the query, the result of any of these functions is `NULL`. If a single input row matches the query, the result of any of these
functions is `"0.0"`.

**Examples:**

This example demonstrates how `VARIANCE()` and `VARIANCE_SAMP()` return the same result, while `VARIANCE_POP()` uses a slightly different calculation to reflect that the input data is considered part of a larger "population".

[localhost:21000] > select variance(score) from test_scores; +-----------------+ | variance(score) | +-----------------+ | 812.25 | +-----------------+ [localhost:21000] > select variance_samp(score) from test_scores; +----------------------+ | variance_samp(score) | +----------------------+ | 812.25 | +----------------------+ [localhost:21000] > select variance_pop(score) from test_scores; +---------------------+ | variance_pop(score) | +---------------------+ | 811.438 | +---------------------+

This example demonstrates that, because the return value of these aggregate functions is a `STRING`, you convert the result with `CAST` if you need to do further calculations as a numeric value.

[localhost:21000] > create table score_stats as select cast(stddev(score) as decimal(7,4)) `standard_deviation`, cast(variance(score) as decimal(7,4)) `variance` from test_scores; +-------------------+ | summary | +-------------------+ | Inserted 1 row(s) | +-------------------+ [localhost:21000] > desc score_stats; +--------------------+--------------+---------+ | name | type | comment | +--------------------+--------------+---------+ | standard_deviation | decimal(7,4) | | | variance | decimal(7,4) | | +--------------------+--------------+---------+

**Restrictions:**

This function cannot be used in an analytic context. That is, the `OVER()` clause is not allowed at all
with this function.

The `STDDEV()`, `STDDEV_POP()`, and `STDDEV_SAMP()` functions compute the standard deviation
(square root of the variance) based on the results of `VARIANCE()`, `VARIANCE_POP()`, and `VARIANCE_SAMP()`
respectively. See STDDEV, STDDEV_SAMP, STDDEV_POP Functions for details about the standard deviation property.

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