What’s the average income at this BBQ?
Ten neighbors have ordinary incomes. Then a guest earning $50 million a year shows up.
No one else at the BBQ got richer. Only the summary changed.
The mean jumped from $86,400 to $4,600,000. The median barely moved, from $80,500 to $87,000.
When someone tells you the “average,” what do you need to know before deciding what it means?
Mean or median?
The mean uses every value, so an extreme value can move it dramatically. The median is the middle value, so it is much less sensitive to a single outlier. Neither is automatically better: the useful measure depends on the question.
Example incomes are invented; the arithmetic is exact.