VARIANCE

Calculate population variance. This function is a synonym for VAR_POP() and returns the variance of a set of values.

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;

• calculating the average of the resulting differences.

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

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 |
+---------+--------+-------+------------------+

See Also

• VAR_POP (equivalent, standard SQL)

• STDDEV_POP (population standard deviation)

• STDDEV_SAMP (sample standard deviation)

_{This page is licensed: GPLv2, originally from fill_help_tables.sql}