Step by step
The question
Question: find the 90th percentile of 6, 8, 9, 11, 12, 14, 15, 17, 18, 20 and 22.
The 90th percentile is a number with about 90% of the data 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: 90/100, times n plus 1.
n is how many numbers: 11.
90/100 is 0.9.
11 plus 1 is 12.
0.9 times 12 is 10.8.
Careful!
The rule uses n plus 1, not n.
That keeps the middle in the middle.
2 Count to the position
10.8 is not whole.
It is between the 10th and the 11th numbers: 20 and 22.
So we take the number halfway between them: add, then divide by 2.
20 plus 22 is 42.
Divided by 2: 21.
3 Check
Let's check: 10 of the 11 numbers are below 21.
That is about 91%, close to 90%.
So it makes sense!
Let's look back.
First: find the position.
Then: count to the position.
Last: check.