SQL is a language that never stops giving, and I’ll probably never stop learning new things about it. I recently stumbled upon the following problem: how to compute the median value of a float array?

Given the following websites table:

Note: I’ll use Postgres syntax to represent arrays, with the rather unconventional curly brackets for people used to web languages. You can also use ARRAY[0.2, 0.4] to declare arrays.

Is there a way to compute the p50 (median value) of the durations arrays in pure SQL for Postgres?

#PERCENTILE_CONT

PostgreSQL features a PERCENTILE_CONT function that computes the percentile of a set of values. Unfortunately, it is a window function, meant to be used over numeric columns.

If duration was a numeric column, we could use the following query:

SELECT PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY duration) AS p50
FROM websites

This would return:

The null value is properly ignored, and rounding is still hard for computers in 2023.

#UNNEST

In our original problem we have arrays of floats. To compute the median value of each array, the solution is to use the UNNEST function, which allows splatting/spreading arrays into rows.

SELECT id, name, UNNEST(durations) AS duration FROM sites

It’s worth noting that id is no longer unique and that empty arrays produce no rows.

We now have a virtual table on which we can use any window function:

SELECT id, PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY duration) AS p50
FROM (
  SELECT id, UNNEST(durations) AS duration FROM sites
) t
GROUP BY id

And then we can LEFT JOIN the websites table to retrieve other details:

SELECT websites.id, name, p50
FROM websites
LEFT JOIN (
	SELECT id, PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY duration) AS p50
	FROM (SELECT id, UNNEST(durations) AS duration FROM sites) t
	GROUP BY id
) t ON t.id = websites.id

Using LEFT JOIN rather than (INNER) JOIN allows us to keep all the websites, even those with an empty array.