# VARIANCE

## Syntax

```VARIANCE(expr)
```

## Description

Returns the population standard variance of `expr`. This is an extension to standard SQL. The standard SQL function 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
• calculate the average of the resulting differences

It is an aggregate function, and so can be used with the GROUP BY clause.

From MariaDB 10.2.2, VARIANCE() can be used as a window function.

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

## Examples

```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:

```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:

```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 |
+---------+--------+-------+------------------+
```