Simple way to calculate median with MySQL

Question

What's the simplest (and hopefully not too slow) way to calculate the median with MySQL? I've used AVG(x) for finding the mean, but I'm having a hard time finding a simple way of calculating the median. For now, I'm returning all the rows to PHP, doing a sort, and then picking the middle row, but surely there must be some simple way of doing it in a single MySQL query.

Example data:

id | val
--------
 1    4
 2    7
 3    2
 4    2
 5    9
 6    8
 7    3

Sorting on val gives 2 2 3 4 7 8 9, so the median should be 4, versus SELECT AVG(val) which == 5.

Answer 1

You could use the user-defined function that's found here.

Answer 2

A comment on this page in the MySQL documentation has the following suggestion:

-- (mostly) High Performance scaling MEDIAN function per group
-- Median defined in http://en.wikipedia.org/wiki/Median
--
-- by Peter Hlavac
-- 06.11.2008
--
-- Example Table:

DROP table if exists table_median;
CREATE TABLE table_median (id INTEGER(11),val INTEGER(11));
COMMIT;


INSERT INTO table_median (id, val) VALUES
(1, 7), (1, 4), (1, 5), (1, 1), (1, 8), (1, 3), (1, 6),
(2, 4),
(3, 5), (3, 2),
(4, 5), (4, 12), (4, 1), (4, 7);



-- Calculating the MEDIAN
SELECT @a := 0;
SELECT
id,
AVG(val) AS MEDIAN
FROM (
SELECT
id,
val
FROM (
SELECT
-- Create an index n for every id
@a := (@a + 1) mod o.c AS shifted_n,
IF(@a mod o.c=0, o.c, @a) AS n,
o.id,
o.val,
-- the number of elements for every id
o.c
FROM (
SELECT
t_o.id,
val,
c
FROM
table_median t_o INNER JOIN
(SELECT
id,
COUNT(1) AS c
FROM
table_median
GROUP BY
id
) t2
ON (t2.id = t_o.id)
ORDER BY
t_o.id,val
) o
) a
WHERE
IF(
-- if there is an even number of elements
-- take the lower and the upper median
-- and use AVG(lower,upper)
c MOD 2 = 0,
n = c DIV 2 OR n = (c DIV 2)+1,

-- if its an odd number of elements
-- take the first if its only one element
-- or take the one in the middle
IF(
c = 1,
n = 1,
n = c DIV 2 + 1
)
)
) a
GROUP BY
id;

-- Explanation:
-- The Statement creates a helper table like
--
-- n id val count
-- ----------------
-- 1, 1, 1, 7
-- 2, 1, 3, 7
-- 3, 1, 4, 7
-- 4, 1, 5, 7
-- 5, 1, 6, 7
-- 6, 1, 7, 7
-- 7, 1, 8, 7
--
-- 1, 2, 4, 1

-- 1, 3, 2, 2
-- 2, 3, 5, 2
--
-- 1, 4, 1, 4
-- 2, 4, 5, 4
-- 3, 4, 7, 4
-- 4, 4, 12, 4


-- from there we can select the n-th element on the position: count div 2 + 1

Answer 3

If MySQL has ROW_NUMBER, then the MEDIAN is (be inspired by this SQL Server query):

WITH Numbered AS 
(
SELECT *, COUNT(*) OVER (ORDER BY val) AS Cnt, ROW_NUMBER() OVER (ORDER BY val) AS RowNum
FROM yourtable
)
SELECT id, val
FROM Numbered
WHERE RowNum IN ((Cnt+1)/2, (Cnt+2)/2)
;

The IN is used in case you have an even number of entries.

If you want to find the median per group, then just PARTITION BY group in your OVER clauses.

Rob

Answer 4

Simple answer : get the value of the following index : count(*) / 2 rounded up.

More complicated answer : count() / 2 rounded up or down depending on your def of median or you can write an if for the even numbered case and avg the middle numbers (the "count() / 2" rounded up number with the "count(*) / 2" rounded down number).

Answer 5

I just found another answer online in the comments:

For medians in almost any SQL:

SELECT x.val from data x, data y
GROUP BY x.val
HAVING SUM(SIGN(1-SIGN(y.val-x.val))) = (COUNT(*)+1)/2

Make sure your columns are well indexed and the index is used for filtering and sorting. Verify with the explain plans.

select count(*) from table --find the number of rows

Calculate the "median" row number. Maybe use: median_row = floor(count / 2).

Then pick it out of the list:

select val from table order by val asc limit median_row,1

This should return you one row with just the value you want.

Jacob

Answer 6

I used a two query approach:

• first one to get count, min, max and avg
• second one (prepared statement) with a "LIMIT @count/2, 1" and "ORDER BY .." clauses to get the median value

These are wrapped in a function defn, so all values can be returned from one call.

If your ranges are static and your data does not change often, it might be more efficient to precompute/store these values and use the stored values instead of querying from scratch every time.