Field note · December 21, 2023
The overall average hides 5 different numbers
Real group means for one column across 5 segments, and what the pooled average conceals.
borough splits ride-hail-trips into 5 groups. Here is what duration_min looks like inside each.
Airport— mean 53.77, median 48.50 (965 rows)Uptown— mean 15.68, median 13.30 (1,453 rows)Midtown— mean 15.62, median 13.20 (2,034 rows)Downtown— mean 15.41, median 13.20 (2,399 rows)Harbour— mean 15.20, median 13.30 (1,149 rows)
Top to bottom that is 53.77 against 15.20, a spread of 253.7%. The pooled average is 20.11.
select borough,
count(*) as rows,
round(avg(duration_min)::numeric, 2) as mean,
percentile_cont(0.5) within group (order by duration_min) as median
from ride_hail_trips
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 Airport 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.