Percentile of 58 in 52, 55, 57, 58, 62, 64, 67, 58, 69, 71, 40, 45 Step by Step

Step by step

The question

Question: what percentile is 58 in 52, 55, 57, 58, 62, 64, 67, 58, 69, 71, 40 and 45?

The percentile of 58 tells what percent of the data is below it.

percentile of 58: 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 58: 5 numbers.

That is x.

Equal to 58: 2.

That is y.

x is 5: the numbers below.

x = 5

y is 2: the numbers equal to 58.

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 12.

percentile = 5 + 0.5 × 212 × 100

5 plus 1 is 6.

percentile = 612 × 100

Careful!

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

Careful: not 712 × 100 ✗

6 divided by 12, times 100, is 50.

So 58 is at the 50th percentile.

percentile = 50

4 Check

Let's check: 5 of 12 are below 58, about 42%.

below 58: 5 of 12 ≈ 42%

7 of 12 are up to 58, about 58%.

up to 58: 7 of 12 ≈ 58%

50 is between them.

So it makes sense!

42 ≤ 50 ≤ 58

Let's look back.

First: put them in order.

Then: count below and equal.

Then: use the rule.

Last: check.

Answer