The overall average hides 6 different numbers

site splits clinical-trial into 6 groups. Here is what baseline_score looks like inside each.

• site-6 — mean 62.19, median 63.10 (146 rows)
• site-1 — mean 61.92, median 62.95 (142 rows)
• site-4 — mean 61.45, median 61.45 (152 rows)
• site-3 — mean 61.04, median 60.75 (148 rows)
• site-2 — mean 60.61, median 60.60 (174 rows)
• site-5 — mean 59.67, median 58.90 (138 rows)

Top to bottom that is 62.19 against 59.67, a spread of 4.2%. The pooled average is 61.14.

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

The groups are close enough that the pooled average is a fair summary. That is worth confirming rather than assuming: the check costs one query and the failure mode is invisible.

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.