# VARIANCE

## Syntax

```sql
VARIANCE(expr)
```

## Description

Returns the population standard variance of `expr`. This is an extension to standard SQL. The standard SQL function [VAR\_POP()](https://mariadb.com/docs/server/reference/sql-functions/aggregate-functions/var_pop) can be used instead.

Variance is calculated by

* working out the mean for the set;
* for each number, subtracting the mean and squaring the result;
* calculating the average of the resulting differences.

It is an [aggregate function](https://mariadb.com/docs/server/reference/sql-functions/aggregate-functions), and so can be used with the [GROUP BY](https://mariadb.com/docs/server/reference/sql-statements/data-manipulation/selecting-data/group-by) clause.

`VARIANCE()` can be used as a [window function](https://mariadb.com/docs/server/reference/sql-functions/special-functions/window-functions).

`VARIANCE()` returns `NULL` if there were no matching rows.

## Examples

```sql
CREATE TABLE v(i tinyint);

INSERT INTO v VALUES(101),(99);

SELECT VARIANCE(i) FROM v;
+-------------+
| VARIANCE(i) |
+-------------+
|      1.0000 |
+-------------+

INSERT INTO v VALUES(120),(80);

SELECT VARIANCE(i) FROM v;
+-------------+
| VARIANCE(i) |
+-------------+
|    200.5000 |
+-------------+
```

As an [aggregate function](https://mariadb.com/docs/server/reference/sql-functions/aggregate-functions):

```sql
CREATE OR REPLACE TABLE stats (category VARCHAR(2), x INT);

INSERT INTO stats VALUES 
  ('a',1),('a',2),('a',3),
  ('b',11),('b',12),('b',20),('b',30),('b',60);

SELECT category, STDDEV_POP(x), STDDEV_SAMP(x), VAR_POP(x) 
  FROM stats GROUP BY category;
+----------+---------------+----------------+------------+
| category | STDDEV_POP(x) | STDDEV_SAMP(x) | VAR_POP(x) |
+----------+---------------+----------------+------------+
| a        |        0.8165 |         1.0000 |     0.6667 |
| b        |       18.0400 |        20.1693 |   325.4400 |
+----------+---------------+----------------+------------+
```

As a [window function](https://mariadb.com/docs/server/reference/sql-functions/special-functions/window-functions):

```sql
CREATE OR REPLACE TABLE student_test (name CHAR(10), test CHAR(10), score TINYINT);

INSERT INTO student_test VALUES 
    ('Chun', 'SQL', 75), ('Chun', 'Tuning', 73), 
    ('Esben', 'SQL', 43), ('Esben', 'Tuning', 31), 
    ('Kaolin', 'SQL', 56), ('Kaolin', 'Tuning', 88), 
    ('Tatiana', 'SQL', 87);

SELECT name, test, score, VAR_POP(score) 
  OVER (PARTITION BY test) AS variance_results FROM student_test;
+---------+--------+-------+------------------+
| name    | test   | score | variance_results |
+---------+--------+-------+------------------+
| Chun    | SQL    |    75 |         287.1875 |
| Chun    | Tuning |    73 |         582.0000 |
| Esben   | SQL    |    43 |         287.1875 |
| Esben   | Tuning |    31 |         582.0000 |
| Kaolin  | SQL    |    56 |         287.1875 |
| Kaolin  | Tuning |    88 |         582.0000 |
| Tatiana | SQL    |    87 |         287.1875 |
+---------+--------+-------+------------------+
```

## See Also

* [VAR\_POP](https://mariadb.com/docs/server/reference/sql-functions/aggregate-functions/var_pop) (equivalent, standard SQL)
* [STDDEV\_POP](https://mariadb.com/docs/server/reference/sql-functions/aggregate-functions/stddev_pop) (population standard deviation)
* [STDDEV\_SAMP](https://mariadb.com/docs/server/reference/sql-functions/aggregate-functions/stddev_samp) (sample standard deviation)

<sub>*This page is licensed: GPLv2, originally from*</sub> [<sub>*fill\_help\_tables.sql*</sub>](https://github.com/MariaDB/server/blob/main/scripts/fill_help_tables.sql)

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