first_response_min by channel: a 11% spread

Breaking first_response_min down by channel on support-tickets, because the headline average is 155 and no segment is actually there.

• in-app — mean 159, median 81 (952 rows)
• phone — mean 152, median 85 (489 rows)
• email — mean 146, median 79 (1,368 rows)
• chat — mean 143, median 77 (1,191 rows)

Top to bottom that is 159 against 143, a spread of 10.8%. The pooled average is 155.

select channel,
  count(*)                                                        as rows,
  round(avg(first_response_min)::numeric, 2)                      as mean,
  percentile_cont(0.5) within group (order by first_response_min) as median
from support_tickets
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 most in in-app, 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.