ASK
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
$0
$50k
$100k
$150k
Median (middle)middle of the ordered values
Mean (average)total ÷ 10
PREDICT
Now someone earning $50 million joins the BBQ.
Your baseline answers carry forward. Predict the two new values.
Baseline median from Ask
$80,500
10 people
Baseline mean from Ask
$86,400
10 people
New guest salary: $50,000,000
New median (middle)
New mean (average)
REVEAL
One barely moves. The other skyrockets.
BEFORE THE GUEST
10 people
$0$1M$2M$3M$4M
$80,500
Median
$86,400
Mean
AFTER THE GUEST
11 people · one earns $50,000,000
$0$1M$2M$3M$4M
$87,000
Median
≈ $4,600,000
Mean
Both panels use the same scale. That is why the first three bars almost disappear.
No one else at the BBQ got richer. But one way of describing the group changed dramatically.
UNDERSTAND
What happens as one salary changes?
The original 10 salaries stay exactly the same. Change only the new guest’s salary.
NEW GUEST SALARY
$0
$0$50,000,000
MEDIAN
$74,000
Follows the middle position.
The guest is still passing through the middle of the group.
MEAN
$78,545
Responds to every value.
The mean changes with every additional dollar.
Median (middle) and mean (average) describe the same group differently.
TRANSFER
“Average ticket price: $50”
Two events can make exactly the same claim.
PRICE LIST A
$36 · $48 · $50 · $54 · $62
PRICE LIST B
$5 · $5 · $5 · $110 · $125
Which list is more helpful?
PRICE LIST A
Mean: $50
Median: $50
PRICE LIST B
Mean: $50
Median: $5
Both have the same mean—but not the same median.
This presents a very different story.
Two service centers each had 6 customers. Both lists have the same average wait time.
CENTER A
10 · 11 · 12 · 12 · 13 · 14
Mean = 12 minutes
CENTER B
1 · 1 · 1 · 1 · 25 · 43
Mean = 12 minutes
What else would you want to know?