Calculate 25th percentile of 2, 4, 5, 7, 8, 10, 11

Step by step

The question

Question: find the 25th percentile of 2, 4, 5, 7, 8, 10 and 11.

The 25th percentile is a number with about 25% 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: 25/100, times n plus 1.

n is how many numbers: 7.

25/100 is 0.25.

7 plus 1 is 8.

0.25 times 8 is 2.

Careful!

The rule uses n plus 1, not n.

2 Count to the position

2 is a whole number.

We count to the 2nd number: 4.

So the 25th percentile is 4.

3 Check

Let's check: 1 of the 7 numbers are below 4.

That is about 14%, close to 25%.

So it makes sense!

Let's look back.

First: find the position.

Then: count to the position.

Last: check.