PostgreSQL 9.4.4 Documentation
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# 9.20. Aggregate Functions

Aggregate functions compute a single result from a set of input values. The built-in normal aggregate functions are listed in Table 9-49 and Table 9-50. The built-in ordered-set aggregate functions are listed in Table 9-51 and Table 9-52. The special syntax considerations for aggregate functions are explained in Section 4.2.7. Consult Section 2.7 for additional introductory information.

Table 9-49. General-Purpose Aggregate Functions

Function | Argument Type(s) | Return Type | Description
--- | --- | --- | ---
`array_agg(`expression`)` | any | array of the argument type | input values, including nulls, concatenated into an array
`avg(`expression`)` | `smallint`, `int`, `bigint`, `real`, `double precision`, `numeric`, or `interval` | `numeric` for any integer-type argument, `double precision` for a floating-point argument, otherwise the same as the argument data type | the average (arithmetic mean) of all input values
`bit_and(`expression`)` | `smallint`, `int`, `bigint`, or `bit` | same as argument data type | the bitwise AND of all non-null input values, or null if none
`bit_or(`expression`)` | `smallint`, `int`, `bigint`, or `bit` | same as argument data type | the bitwise OR of all non-null input values, or null if none
`bool_and(`expression`)` | `bool` | `bool` | true if all input values are true, otherwise false
`bool_or(`expression`)` | `bool` | `bool` | true if at least one input value is true, otherwise false
`count(*)` |  | `bigint` | number of input rows
`count(`expression`)` | any | `bigint` | number of input rows for which the value of `expression` is not null
`every(`expression`)` | `bool` | `bool` | equivalent to `bool_and`
`json_agg(`expression`)` | `any` | `json` | aggregates values as a JSON array
`json_object_agg(`name`, `value`)` | `(any, any)` | `json` | aggregates name/value pairs as a JSON object
`max(`expression`)` | any array, numeric, string, or date/time type | same as argument type | maximum value of `expression` across all input values
`min(`expression`)` | any array, numeric, string, or date/time type | same as argument type | minimum value of `expression` across all input values
`string_agg(`expression`, `delimiter`)` | (`text`, `text`) or (`bytea`, `bytea`) | same as argument types | input values concatenated into a string, separated by delimiter
`sum(`expression`)` | `smallint`, `int`, `bigint`, `real`, `double precision`, `numeric`, `interval`, or `money` | `bigint` for `smallint` or `int` arguments, `numeric` for `bigint` arguments, otherwise the same as the argument data type | sum of `expression` across all input values
`xmlagg(`expression`)` | `xml` | `xml` | concatenation of XML values (see also Section 9.14.1.7)

It should be noted that except for `count`, these functions return a null value when no rows are selected. In particular, `sum` of no rows returns null, not zero as one might expect, and `array_agg` returns null rather than an empty array when there are no input rows. The `coalesce` function can be used to substitute zero or an empty array for null when necessary.

> Note: Boolean aggregates `bool_and` and `bool_or` correspond to standard SQL aggregates `every` and `any` or `some`. As for `any` and `some`, it seems that there is an ambiguity built into the standard syntax:

>     SELECT b1 = ANY((SELECT b2 FROM t2 ...)) FROM t1 ...;

> Here `ANY` can be considered either as introducing a subquery, or as being an aggregate function, if the subquery returns one row with a Boolean value. Thus the standard name cannot be given to these aggregates.

> Note: Users accustomed to working with other SQL database management systems might be disappointed by the performance of the `count` aggregate when it is applied to the entire table. A query like:

>     SELECT count(*) FROM sometable;

> will require effort proportional to the size of the table: PostgreSQL will need to scan either the entire table or the entirety of an index which includes all rows in the table.

The aggregate functions `array_agg`, `json_agg`, `json_object_agg`, `string_agg`, and `xmlagg`, as well as similar user-defined aggregate functions, produce meaningfully different result values depending on the order of the input values. This ordering is unspecified by default, but can be controlled by writing an `ORDER BY` clause within the aggregate call, as shown in Section 4.2.7. Alternatively, supplying the input values from a sorted subquery will usually work. For example:

    SELECT xmlagg(x) FROM (SELECT x FROM test ORDER BY y DESC) AS tab;

But this syntax is not allowed in the SQL standard, and is not portable to other database systems.

Table 9-50 shows aggregate functions typically used in statistical analysis. (These are separated out merely to avoid cluttering the listing of more-commonly-used aggregates.) Where the description mentions `N`, it means the number of input rows for which all the input expressions are non-null. In all cases, null is returned if the computation is meaningless, for example when `N` is zero.

Table 9-50. Aggregate Functions for Statistics

Function | Argument Type | Return Type | Description
--- | --- | --- | ---
`corr(`Y`, `X`)` | `double precision` | `double precision` | correlation coefficient
`covar_pop(`Y`, `X`)` | `double precision` | `double precision` | population covariance
`covar_samp(`Y`, `X`)` | `double precision` | `double precision` | sample covariance
`regr_avgx(`Y`, `X`)` | `double precision` | `double precision` | average of the independent variable (`sum(`X`)/`N``)
`regr_avgy(`Y`, `X`)` | `double precision` | `double precision` | average of the dependent variable (`sum(`Y`)/`N``)
`regr_count(`Y`, `X`)` | `double precision` | `bigint` | number of input rows in which both expressions are nonnull
`regr_intercept(`Y`, `X`)` | `double precision` | `double precision` | y-intercept of the least-squares-fit linear equation determined by the (`X`, `Y`) pairs
`regr_r2(`Y`, `X`)` | `double precision` | `double precision` | square of the correlation coefficient
`regr_slope(`Y`, `X`)` | `double precision` | `double precision` | slope of the least-squares-fit linear equation determined by the (`X`, `Y`) pairs
`regr_sxx(`Y`, `X`)` | `double precision` | `double precision` | `sum(`X`^2) - sum(`X`)^2/`N`` ("sum of squares" of the independent variable)
`regr_sxy(`Y`, `X`)` | `double precision` | `double precision` | `sum(`X`*`Y`) - sum(`X`) * sum(`Y`)/`N`` ("sum of products" of independent times dependent variable)
`regr_syy(`Y`, `X`)` | `double precision` | `double precision` | `sum(`Y`^2) - sum(`Y`)^2/`N`` ("sum of squares" of the dependent variable)
`stddev(`expression`)` | `smallint`, `int`, `bigint`, `real`, `double precision`, or `numeric` | `double precision` for floating-point arguments, otherwise `numeric` | historical alias for `stddev_samp`
`stddev_pop(`expression`)` | `smallint`, `int`, `bigint`, `real`, `double precision`, or `numeric` | `double precision` for floating-point arguments, otherwise `numeric` | population standard deviation of the input values
`stddev_samp(`expression`)` | `smallint`, `int`, `bigint`, `real`, `double precision`, or `numeric` | `double precision` for floating-point arguments, otherwise `numeric` | sample standard deviation of the input values
`variance`(`expression`) | `smallint`, `int`, `bigint`, `real`, `double precision`, or `numeric` | `double precision` for floating-point arguments, otherwise `numeric` | historical alias for `var_samp`
`var_pop`(`expression`) | `smallint`, `int`, `bigint`, `real`, `double precision`, or `numeric` | `double precision` for floating-point arguments, otherwise `numeric` | population variance of the input values (square of the population standard deviation)
`var_samp`(`expression`) | `smallint`, `int`, `bigint`, `real`, `double precision`, or `numeric` | `double precision` for floating-point arguments, otherwise `numeric` | sample variance of the input values (square of the sample standard deviation)

Table 9-51 shows some aggregate functions that use the ordered-set aggregate syntax. These functions are sometimes referred to as "inverse distribution" functions.

Table 9-51. Ordered-Set Aggregate Functions

Function | Direct Argument Type(s) | Aggregated Argument Type(s) | Return Type | Description
--- | --- | --- | --- | ---
`mode() WITHIN GROUP (ORDER BY `sort_expression`)` |  | any sortable type | same as sort expression | returns the most frequent input value (arbitrarily choosing the first one if there are multiple equally-frequent results)
`percentile_cont(`fraction`) WITHIN GROUP (ORDER BY `sort_expression`)` | `double precision` | `double precision` or `interval` | same as sort expression | continuous percentile: returns a value corresponding to the specified fraction in the ordering, interpolating between adjacent input items if needed
`percentile_cont(`fractions`) WITHIN GROUP (ORDER BY `sort_expression`)` | `double precision[]` | `double precision` or `interval` | array of sort expression's type | multiple continuous percentile: returns an array of results matching the shape of the `fractions` parameter, with each non-null element replaced by the value corresponding to that percentile
`percentile_disc(`fraction`) WITHIN GROUP (ORDER BY `sort_expression`)` | `double precision` | any sortable type | same as sort expression | discrete percentile: returns the first input value whose position in the ordering equals or exceeds the specified fraction
`percentile_disc(`fractions`) WITHIN GROUP (ORDER BY `sort_expression`)` | `double precision[]` | any sortable type | array of sort expression's type | multiple discrete percentile: returns an array of results matching the shape of the `fractions` parameter, with each non-null element replaced by the input value corresponding to that percentile

All the aggregates listed in Table 9-51 ignore null values in their sorted input. For those that take a `fraction` parameter, the fraction value must be between 0 and 1; an error is thrown if not. However, a null fraction value simply produces a null result.

Each of the aggregates listed in Table 9-52 is associated with a window function of the same name defined in Section 9.21. In each case, the aggregate result is the value that the associated window function would have returned for the "hypothetical" row constructed from `args`, if such a row had been added to the sorted group of rows computed from the `sorted_args`.

Table 9-52. Hypothetical-Set Aggregate Functions

Function | Direct Argument Type(s) | Aggregated Argument Type(s) | Return Type | Description
--- | --- | --- | --- | ---
`rank(`args`) WITHIN GROUP (ORDER BY `sorted_args`)` | `VARIADIC` `"any"` | `VARIADIC` `"any"` | `bigint` | rank of the hypothetical row, with gaps for duplicate rows
`dense_rank(`args`) WITHIN GROUP (ORDER BY `sorted_args`)` | `VARIADIC` `"any"` | `VARIADIC` `"any"` | `bigint` | rank of the hypothetical row, without gaps
`percent_rank(`args`) WITHIN GROUP (ORDER BY `sorted_args`)` | `VARIADIC` `"any"` | `VARIADIC` `"any"` | `double precision` | relative rank of the hypothetical row, ranging from 0 to 1
`cume_dist(`args`) WITHIN GROUP (ORDER BY `sorted_args`)` | `VARIADIC` `"any"` | `VARIADIC` `"any"` | `double precision` | relative rank of the hypothetical row, ranging from 1/`N` to 1

For each of these hypothetical-set aggregates, the list of direct arguments given in `args` must match the number and types of the aggregated arguments given in `sorted_args`. Unlike most built-in aggregates, these aggregates are not strict, that is they do not drop input rows containing nulls. Null values sort according to the rule specified in the `ORDER BY` clause.

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