Percentile

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

Formula

Formula

(percentile) = [nless + 0.5⋅nequal]/n

(percentile): Percentile Rank
nless: Number of values less than 'wanted'
nequal: 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.