Percentile of 7 in 3, 7, 4, 9, 7, 6, 8, 10, 5, 2 Step by Step

Step by step

The question

Question: what percentile is 7 in 3, 7, 4, 9, 7, 6, 8, 10, 5 and 2?

The percentile of 7 tells what percent of the data is below it.

percentile of 7: the percent 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 Count below and equal

Below 7: 5 numbers.

That is x.

Equal to 7: 2.

That is y.

x is 5: the numbers below.

x = 5

y is 2: the numbers equal to 7.

y = 2

3 Use the rule

The rule: x plus half of y, over n, times 100.

Half of y: the equal ones count half below.

percentile = x + 0.5yn × 100

We put the numbers in: x is 5, y is 2, n is 10.

percentile = 5 + 0.5 × 210 × 100

5 plus 1 is 6.

percentile = 610 × 100

Careful!

Not all of the equal ones: only half of y counts as below.

Careful: not 710 × 100 ✗

6 divided by 10, times 100, is 60.

So 7 is at the 60th percentile.

percentile = 60

4 Check

Let's check: 5 of 10 are below 7, about 50%.

below 7: 5 of 10 ≈ 50%

7 of 10 are up to 7, about 70%.

up to 7: 7 of 10 ≈ 70%

60 is between them.

So it makes sense!

50 ≤ 60 ≤ 70

Let's look back.

First: put them in order.

Then: count below and equal.

Then: use the rule.

Last: check.

Answer