# Percentile

How to find the percentile rank of the value for the given data: formula, 2 examples, and their solutions.

## Formula

### Formula

(percentile) = [n_{less} + 0.5⋅n_{equal}]/n

(percentile): Percentile Rank

n_{less}: Number of values less than 'wanted'

n_{equal}: Number of 'wanted'

n: Total number of values

## Example 1

### Example

### Solution

There are 6 values

that are less than 4.

And there's 1 of 4.

So the percentile rank is,

the number of values less than 4, 6

plus

0.5 times, the number of 4, 1

over,

the total number of values, 20

times 100.

So (percentile) = [(6 + 0.5⋅1)/20]⋅100.

6 + 0.5⋅1

= 6 + 0.5

= 6.5

Cancel the denominator 20

and reduce 100 to, 100/20, 5.

6.5⋅5 = 32.5

(percentile) = 32.5

The percentile is usually written

without decimals.

So round 32.5 to the nearest ones.

The tenth is 5.

So add 1 to the ones 2:

1 + 2 = 3.

So the value 4 is

at the 33rd percentile rank.

So [33rd percentile] is the answer.

## Example 2

### Example

### Solution

There are 12 values

that are less than 7.

And there's 4 of 7-s.

So the percentile rank is,

the number of values less than 7, 12

plus

0.5 times, the number of 7, 4

over,

the total number of values, 20

times 100.

So (percentile) = [(12 + 0.5⋅4)/20]⋅100.

+0.5⋅4 = +2

12 + 2 = 14

14/20 = 7/10

Cancel the denominator 10

and reduce 100 to, 100/10, 10.

7⋅10 = 70

(percentile) = 70

So the value 7 is

at the 70th percentile rank.

So [70th percentile] is the answer.