Step by step
The question
Question: find the 80th percentile of 5, 7, 8, 10, 12, 13, 15, 18 and 20.
The 80th percentile is a number with about 80% of the data below it.
80th percentile: about 80% are below it
They are already in order.
Small green numbers count the positions: 1, 2, 3, and so on.
1 Find the position
The position i: 80/100, times n plus 1.
n is how many numbers: 9.
i = 80100 × (n + 1)
80/100 is 0.8.
9 plus 1 is 10.
i = 0.8 × 10
0.8 times 10 is 8.
i = 8
Careful!
The rule uses n plus 1, not n.
That keeps the middle in the middle.
Careful: not 0.8 × 9 ✗
2 Count to the position
8 is a whole number.
We count to the 8th number: 18.
So the 80th percentile is 18.
P80 = 18
3 Check
Let's check: 7 of the 9 numbers are below 18.
That is about 78%, close to 80%.
So it makes sense!
below 18: 7 of 9 = 78% ≈ 80%
Let's look back.
First: find the position.
Then: count to the position.
Last: check.
Answer
P80 = 18