Step by step
The question
Question: what percentile is 24 in 15, 18, 20, 22, 24, 26, 27, 29, 31 and 35?
The percentile of 24 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 24: 4 numbers.
That is x.
Equal to 24: 1.
That is y.
x is 4: the numbers below.
y is 1: the numbers equal to 24.
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 24 is at the 45th percentile.
3 Check
Let's check: 4 of 10 are below 24, about 40%.
5 of 10 are up to 24, 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.