Calculate 40th percentile of 31, 25, 28, 40, 36, 22, 33, 30, 27

Step by step

The question

Question: find the 40th percentile of 31, 25, 28, 40, 36, 22, 33, 30 and 27.

The 40th percentile is a number with about 40% of the data below it.

1 Put them in order

In order, smallest to biggest.

Small green numbers count the positions: 1, 2, 3, and so on.

2 Find the position

The position i: 40/100, times n plus 1.

n is how many numbers: 9.

40/100 is 0.4.

9 plus 1 is 10.

0.4 times 10 is 4.

Careful!

The rule uses n plus 1, not n.

3 Count to the position

4 is a whole number.

We count to the 4th number: 28.

So the 40th percentile is 28.

4 Check

Let's check: 3 of the 9 numbers are below 28.

That is about 33%, close to 40%.

So it makes sense!

Let's look back.

First: put them in order.

Then: find the position.

Then: count to the position.

Last: check.