Calculate 65th percentile of 72, 65, 80, 77, 69, 85, 90, 74, 68, 83 Step by Step

Step by step

The question

Question: find the 65th percentile of 72, 65, 80, 77, 69, 85, 90, 74, 68 and 83.

The 65th percentile is a number with about 65% of the data below it.

65th percentile: about 65% are 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: 65/100, times n plus 1.

n is how many numbers: 10.

i = 65100 × (n + 1)

65/100 is 0.65.

10 plus 1 is 11.

i = 0.65 × 11

0.65 times 11 is 7.15.

i = 7.15

Careful!

The rule uses n plus 1, not n.

That keeps the middle in the middle.

Careful: not 0.65 × 10 ✗

3 Count to the position

7.15 is not whole.

It is between the 7th and the 8th numbers: 80 and 83.

So we take the number halfway between them: add, then divide by 2.

P65 = 80 + 832

80 plus 83 is 163.

Divided by 2: 81.5.

P65 = 81.5

4 Check

Let's check: 7 of the 10 numbers are below 81.5.

That is about 70%, close to 65%.

So it makes sense!

below 81.5: 7 of 10 = 70% ≈ 65%

Let's look back.

First: put them in order.

Then: find the position.

Then: count to the position.

Last: check.

Answer