A score is usually difficult to interpret. If your score in a exam was 70 out of 150 then you will have a very little idea how good you are compared to others. It will be more relevant if you can know the percentage of people with lower score than yours.

This percentage is known as percentile. Percentile is a value below which a percentage of data falls. It gives an idea of what percent of other scores are less than the data points investigated. One of the values of a statistical variable that divides the distribution of the variable into 100 groups having equal frequencies. Percentile is commonly also known as centile.

For Example : If the height of a person is 1.92m then 1.92m will be the 90th percentile in the given group. They measure the position from bottom.

## Percentile Rank Formula

Percentile ranks are normally distributed and are not on an equal interval scale. Given below is the formula to find the percentile rank of a score.
Formula for percentile rank:

Percentile rank = $\frac{Number\ of\ scores\ below\ x}{n}$ * 100

Here x out of a set n scores are considered where x is not included.

## Class Percentile

Class percentile determines a student's performance based on the other students in a particular class. To find we need to gather the scores in a given class from highest to the lowest.
Given below are the steps to be followed for finding class rank:
1) Find the number of people in your class and find out what is your rank among your classmates.
2) Divide your numerical rank by the total number of students in the class.
For example, if you hold a rank of 15 among 200 students then $\frac{15}{200}$ = 0.075
3) Convert the obtained decimal into a percentage by multiplying the above result by 100.
In the above example when you multiply 0.075 by 100 you get 7.5%. So you are among the 8% of your class.

## Percentile Rank

Percentage of scores that fall at or below a given score is known as percentile rank. Usually written to the nearest whole percent and are divided into 100 equally sized groups. The lowest score is at the first percentile and the highest score is at the 99th percentile.

The results may be misleading if you try to compute the mean of percentile scores. For example: If 70% of the scores is below yours then your score would be the 70th percentile. Using percentile ranks we can easily convey an individual's standing at graduation relative to other graduates. Scores are arranged in rank order from lowest to highest.

Percentile rankings are based on the cumulative rankings of full time students in each class. Transferred students are not included. Percentage rankings are used to approximate their standard relative to their classmates.

 Percentile Cumulative GPA Range Top 5 % 3.73 - 4 Top 10% 3.65 - 4 Top 25% 3.36 - 4 Top 50% 3.06 - 4 Top 75% 2.85 - 4 Top 90% 2.54 - 4

## Standard Deviation Percentile

Each standard deviation represents a certain percentile. We can find the percentiles when standard deviation and mean is given. When two decimal places are used -3 is the 0.13th percentile, o represents 50th percentile, 1 is the 84.13th percentile, 2 will be 97.72th percentile, 3 is the 99.87th percentile.
If a Z score is given then we can easily find the standard deviation using the below formula:

Z = $\frac{Score - Mean}{S.D}$

## Normal Distribution Percentile

For a normal distribution, the percentile can be calculated from the z-score. These value of the percentile for each z-score can be found in various tables. A system of equations helps in finding both the mean and the standard deviation.

It is easy to find the z score if you know the mean and standard deviation. With the help of statistical tables one can easily compute the area to the left or right of any given z score. Area obtained is the percentile. They are normal equivalents and are uniform and rectangular in shape.

## Percentile Rank Problems

Given below are the problems based on percentile rank:

Example 1 : Find the percentile rank of David, where he ranks out to be 18 among 500 students.

Solution : David is ranked to be 18th.

Formula to find percentile rank is

Percentile rank = $\frac{Number\ of\ scores\ below\ x}{n}$ * 100

$\frac{18}{500}$ * 100

= 0.036 $\times$ 100
= 3.6
David's standing in the class is 3.6th percentile.

Example 2 : If Michelle's rank is 25 among 100 students find out what would be her percentile rank?

Solution : Given, Michelle's rank  = 25

Total number of students in the class = 100

Formula to find percentile rank is

Percentile rank = $\frac{Number\ of\ scores\ below\ x}{n}$ * 100

$\frac{25}{100}$ * 100

= 0.25 $\times$ 100
= 25
Michelle's percentile rank is 25.