salary_max_usd by city: a 427% spread

Breaking salary_max_usd down by city on data-job-postings, because the headline average is 138,807 and no segment is actually there.

• San Francisco — mean 176,026, median 174,250 (532 rows)
• New York — mean 168,826, median 172,500 (495 rows)
• Austin — mean 138,919, median 140,500 (253 rows)
• Chicago — mean 134,973, median 137,000 (299 rows)
• London — mean 85,831, median 92,000 (436 rows)
• Amsterdam — mean 83,441, median 92,500 (245 rows)

Top to bottom that is 176,026 against 33,385, a spread of 427.3%. The pooled average is 138,807.

select city,
  count(*)                                                    as rows,
  round(avg(salary_max_usd)::numeric, 2)                      as mean,
  percentile_cont(0.5) within group (order by salary_max_usd) as median
from data_job_postings
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 San Francisco 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 only slightly here. 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.