The overall average hides 8 different numbers

industry splits saas-subscriptions into 8 groups. Here is what seats_now looks like inside each.

• finance — mean 72, median 6 (293 rows)
• public sector — mean 66, median 8 (334 rows)
• media — mean 60, median 8 (296 rows)
• software — mean 59, median 10 (326 rows)
• healthcare — mean 58, median 12 (334 rows)
• retail — mean 58, median 11 (314 rows)

Top to bottom that is 72 against 46, a spread of 57.1%. The pooled average is 59.

select industry,
  count(*)                                               as rows,
  round(avg(seats_now)::numeric, 2)                      as mean,
  percentile_cont(0.5) within group (order by seats_now) as median
from saas_subscriptions
group by 1
order by mean desc;

A spread that wide means the pooled number is not a summary, it is an artefact of the mix. Change the proportion of finance rows and the overall average moves without any individual group changing at all — which is how a metric goes up while every segment goes down.

Notice the mean and median columns disagree most in finance, where the mean sits well above the median. Always compute both in the group-by. The comparison between them per segment is free and tells you whether you are looking at a level difference or a tail difference.

This is the setup for Simpson's paradox — the case where every segment moves one way and the total moves the other.