population by region: a 63% spread

Breaking population down by region on world-indicators, because the headline average is 130,641,222 and no segment is actually there.

• Americas — mean 162,193,332, median 165,799,999 (144 rows)
• Asia — mean 153,218,098, median 154,507,140 (168 rows)
• Africa — mean 123,677,258, median 124,790,250 (144 rows)
• Oceania — mean 112,462,161, median 122,674,867 (72 rows)
• Europe — mean 99,262,493, median 110,574,882 (192 rows)

Top to bottom that is 162,193,332 against 99,262,493, a spread of 63.4%. The pooled average is 130,641,222.

select region,
  count(*)                                                as rows,
  round(avg(population)::numeric, 2)                      as mean,
  percentile_cont(0.5) within group (order by population) as median
from world_indicators
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 Americas 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.