Where is the middle — and what is the mean?
Ten people are at a backyard BBQ. Use the graph to estimate both measures.
Annual salaries of the 10 guests
Now someone earning $50 million joins the BBQ.
The other 10 salaries stay the same. Predict the two new values.
New median
Was $80,500 with 10 people
New mean
Was $86,400 with 10 people
One barely moves. The other skyrockets.
Both panels use the same scale.
BEFORE THE GUEST
10 people
AFTER THE GUEST
11 people · one earns $50,000,000
No one else at the BBQ got richer. But one way of describing the group changed dramatically.
What happens as one salary changes?
The original 10 salaries stay the same. Change only the new guest’s salary.
When people hear “average,” they usually picture someone typical — near the middle. But the reported average is usually the mean, and one extreme value can pull it far from typical.
“Average ticket price: $50”
Two events make exactly the same claim.
PRICE LIST A
PRICE LIST B
Where does a typical ticket actually cost about $50?
Same mean. Very different medians.
At Event B, most tickets cost $5. Two expensive tickets pull the mean up to $50 — a price no one there actually paid.
DINNER ORDERS
They split the bill evenly. Which number tells each friend what to pay?
This time, the mean is the number you need.
An even split is exactly what the mean does: share the total equally. Paying the median, $10 each, would leave $50 unpaid. Typical? Use the middle. Fair share of a total? Use the mean.