How to calculate the population standard variance of a field expression in result set groups using the VAR_POP() function?

VAR_POP(expr) is a MySQL built-in aggregate function that calculates the population standard variance of a field expression in result set groups. For example:

SELECT help_category_id, VAR_POP(help_topic_id), COUNT(help_topic_id)
  FROM mysql.help_topic GROUP BY help_category_id;
  -- +------------------+------------------------+----------------------+
  -- | help_category_id | VAR_POP(help_topic_id) | COUNT(help_topic_id) |
  -- +------------------+------------------------+----------------------+
  -- |                1 |                   0.25 |                    2 |
  -- |                2 |     105.16408163265307 |                   35 |
  -- |                3 |      7175.054869290432 |                   59 |
  -- |                4 |                   0.25 |                    2 |
  -- |                5 |      2.888888888888887 |                    3 |
  -- ...
  -- +------------------+------------------------+----------------------+

SELECT help_category_id, help_topic_id
  FROM mysql.help_topic WHERE help_category_id = 5;
  -- +------------------+---------------+
  -- | help_category_id | help_topic_id |
  -- +------------------+---------------+
  -- |                5 |            40 |
  -- |                5 |            43 |
  -- |                5 |            44 |
  -- +------------------+---------------+

VAR_POP() is also a window function, you can call it with the OVER clause to calculate the population standard variance of the given expression in the current window. For example:

SELECT help_topic_id, help_category_id, 
  VAR_POP(help_topic_id) OVER w
  FROM mysql.help_topic 
  WINDOW w AS (PARTITION BY help_category_id);
  -- +---------------+------------------+-------------------------------+
  -- | help_topic_id | help_category_id | VAR_POP(help_topic_id) OVER w |
  -- +---------------+------------------+-------------------------------+
  -- |             0 |                1 |                          0.25 |
  -- |             1 |                1 |                          0.25 |
  -- |             2 |                2 |            105.16408163265307 |
  -- |             6 |                2 |            105.16408163265307 |
  -- |             7 |                2 |            105.16408163265307 |
  -- |             8 |                2 |            105.16408163265307 |
  -- |             9 |                2 |            105.16408163265307 |
  -- ...
  -- +---------------+------------------+-------------------------------+

Reference information of the VAR_POP() function:

VAR_POP(expr): var
  Returns the population standard variance of expr. It considers rows as
  the whole population, not as a sample, so it has the number of rows as
  the denominator. If there are no matching rows, VAR_POP() returns NULL.

Arguments, return value and availability:
  expr: Required. The field expression in result set groups.
  var: Return value. The population standard variance of the input expression.
  Available since MySQL 5.7.

Related MySQL functions:

• VAR_SAMP() - Sample Standard Variance
• VARIANCE() - Synonym for VAR_POP()

⇒ VAR_SAMP() - Sample Standard Variance

⇐ SUM() - Total Value in Group

⇑ MySQL Functions on Aggregation Groups

⇑⇑ MySQL Function References