PostgreSQL provides two functions to calculate percentiles for a list of values at any percentage: percentile_cont() and percentile_disc(). With the correct argument, both functions can be used to compute the median.

• The percentile_disc() function returns the closest value from the input set that corresponds to the requested percentile. The result is always a value that exists in the set.
• The percentile_cont() function returns an interpolated value based on the distribution of the dataset. It provides a more precise result, but the returned value may be a fractional number that does not directly exist in the input set.

Both functions can be used as shown in the following snippet:

SELECT
  percentile_disc(0.5) WITHIN GROUP (ORDER BY temperature)
FROM city_data;

Here, 0.5 represents the 50th percentile, which corresponds to the median. The WITHIN GROUP clause specifies the order of values before computing the percentile.