Step by step
The question
Question: what percentile is 9 in 2, 4, 5, 7, 9, 11, 12, 14, 15 and 18?
The percentile of 9 tells what percent of the data is below it.
They are already in order.
Small green numbers count the positions: 1, 2, 3, and so on.
1 Count below and equal
Below 9: 4 numbers.
That is x.
Equal to 9: 1.
That is y.
x is 4: the numbers below.
y is 1: the numbers equal to 9.
2 Use the rule
The rule: x plus half of y, over n, times 100.
Half of y: the equal ones count half below.
We put the numbers in: x is 4, y is 1, n is 10.
4 plus 0.5 is 4.5.
Careful!
Not all of the equal ones: only half of y counts as below.
4.5 divided by 10, times 100, is 45.
So 9 is at the 45th percentile.
3 Check
Let's check: 4 of 10 are below 9, about 40%.
5 of 10 are up to 9, about 50%.
45 is between them.
So it makes sense!
Let's look back.
First: count below and equal.
Then: use the rule.
Last: check.