Step by step
The question
Question: find the 35th percentile of 14, 17, 19, 20, 22, 25, 26, 28, 30, 33, 35 and 38.
The 35th percentile is a number with about 35% 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: 35/100, times n plus 1.
n is how many numbers: 12.
35/100 is 0.35.
12 plus 1 is 13.
0.35 times 13 is 4.55.
Careful!
The rule uses n plus 1, not n.
That keeps the middle in the middle.
2 Count to the position
4.55 is not whole.
It is between the 4th and the 5th 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: 4 of the 12 numbers are below 21.
That is about 33%, close to 35%.
So it makes sense!
Let's look back.
First: find the position.
Then: count to the position.
Last: check.