Percentile of 30 in 30, 25, 18, 30, 40, 35, 22, 30, 28, 45, 33, 20 Step by Step

Step by step

The question

Question: what percentile is 30 in 30, 25, 18, 30, 40, 35, 22, 30, 28, 45, 33 and 20?

The percentile of 30 tells what percent of the data is below it.

percentile of 30: 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 30: 5 numbers.

That is x.

Equal to 30: 3.

That is y.

x is 5: the numbers below.

x = 5

y is 3: the numbers equal to 30.

y = 3

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 3, n is 12.

percentile = 5 + 0.5 × 312 × 100

5 plus 1.5 is 6.5.

percentile = 6.512 × 100

Careful!

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

Careful: not 812 × 100 ✗

6.5 divided by 12, times 100, is about 54.2.

percentile ≈ 54.2…

to the nearest whole number

To the nearest whole number: 54.

So 30 is at the 54th percentile.

percentile ≈ 54

4 Check

Let's check: 5 of 12 are below 30, about 42%.

below 30: 5 of 12 ≈ 42%

8 of 12 are up to 30, about 67%.

up to 30: 8 of 12 ≈ 67%

54 is between them.

So it makes sense!

42 ≤ 54 ≤ 67

Let's look back.

First: put them in order.

Then: count below and equal.

Then: use the rule.

Last: check.

Answer