Percentile Formula

What is Percentile?

What is percentile?  Mostly we can define percentile as a number where a certain percentage of scores fall below that given number. Percentile and percentage are often confused but both are different concepts. The percentage used to express fractions of a whole, while percentiles are the values below which a certain percentage of the data in a data set is found. If you want to know where you stand compared to the rest of the crowd, you need a statistic that reports relative standing, and that statistic is called a percentile.

For example, you are the fourth tallest person in a group of 20.80% of people are shorter than you. That means you are at the 80th percentile.

If your height is 5.4inch then "5.4 inch" is the 80th percentile height in that group.

Percentile Formula is given as -


Percentile = \[\frac{n}{N}\] x 100


Where, n =ordinal rank of a given value 

 N = number of values in the data set,

 P = Percentile


Formula for Percentile

In mathematics, we use this term percentile informally to indicate that a certain percentage falls below that percentile value. For example, if we score in the 25th percentile, then 25% of test-takers are below this score. Here 25 is called the percentile rank. Percentile divides a data set into the 100 equal parts. A percentile is a measurement that tells us what percent of the total frequency of a data set was at or below that measure. As an example, let us consider a student’s percentile in some exams.

If on this test, a given student scored in the 60th percentile on the quantitative section, she scored at or better than 60% of the other students. Further, if a total of 500 students took the test, then this student scored at or better than 

500×0.60=300 students out of 500 students. In other words, 200 students scored better than that particular student.

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Therefore, percentiles are used to understand and interpret the given data. They also indicate the values below which a certain percentage of the data in a data set is found. Percentiles are frequently useful to understand the test scores and biometric measurements in our day-to-day routine.

Percentile is calculated by the ratio of the number of values below ‘x’ to the total number of values.


Formula for Percentile

The Percentile Formula is given as,


Percentile (P) = (Number of Values Below “x” / Total Number of Values) × 100


Procedure to Calculate Kth Percentile 

The kth percentile is a value in a data set that divides the data into two parts. The lower part contains k percent of the data, and the upper part contains the rest of the data.

The following are the steps to calculate the kth percentile (where k is any number between zero and one hundred).


Step 1: Arrange all data values in the data set in ascending order.


Step 2: Count the number of values in the data set where it is represented as 'n'.


Step 3: calculate the value of k /100, where k = any number between zero and one hundred.


Step 4: Multiply 'k' percent by 'n'.The resultant number is called an index.


Step 5: If the resultant index is not a whole number then round to the nearest whole number, then go to Step 7. If the index is a whole number, then go to Step 6. 


Step 6: Count the values in your data set from left to right until you reach the number. Then find the mean for that corresponding number and the next number. The resultant value is the kth percentile of your data set. 


Step 7: Count the values in your data set from left to right until you reach the number. The obtained value will be the kth percentile of your data set.


Solved Examples

Percentile formula example.


Example 1:

Let us consider the percentile example problem: In a college, a list of grades of 15 students has been declared. Their grades are given as: 85, 34, 42, 51, 84, 86, 78, 85, 87, 69, 74, 65. Find the 80th percentile?

Solution:

Step 1:

Arrange the data in ascending order. 

Let us arrange in Ascending Order = 34, 42, 51, 65, 69, 74, 78, 84, 85, 85, 86, 87.

Step 2:

Find Rank,

Rank = Percentile / 100 

= 80 / 100

k = 0.80

Step 3:

Find 80th percentile,

80th percentile = 0.80 x 12 

= 9.6

Step 4:

Since it is not a whole number, round to the nearest whole number. 

Therefore, 9.6 is rounded to 10. 

Now, Count the values from left to right in the given data set until you reach the number 10.

From the given data set, 10th number is 85.

Therefore, 80th percentile of given data set is 85


Example 2: The scores for students are 40, 45, 49, 53, 61, 65, 71, 79, 85, 91. What is the percentile for score 71?

Solution: We have,

No. of. scores below 71 = 6 Total no. of. scores = 10 

The formula for percentile is given as,

Percentile = (Number of Values Below “x” / Total Number of Values) × 100 = \[\frac{n}{N}\]x 100

Percentile of 71= 6/10 × 100

= 0.6 × 100 = 60

FAQ (Frequently Asked Questions)

1. What is the Percentile Rank Formula?   

Answer: Percentile Rank is a usual term mainly used in statistics which is arrived from Percentile. Percentile (also referred to as Centile) is the percentage of scores that range between 0 and 100 which is less than or equal to the given set of distribution. Percentiles divide any distribution into 100 equal parts. This is predominantly used for the interpretation of scores with different ranges across various tests. Percentile Rank formula (PR) is arrived based on the total number of ranks and the number of ranks below and above percentile.

A Percentile Rank formula is given by:

Percentile Rank (PR) = [(M + (0.5 * R)) / Y] x 100

Where,

  • M = Number of Ranks below x

  • R = Number of Ranks equals x

  • Y = Total Number of Ranks

2. What is the Percentile Range?

Answer: A percentile range is a difference between two specified percentiles. These could theoretically be any two percentiles, but the 10-90 percentile range is the most common. To find the 10-90 percentile range:

  1. Calculate the 10th percentile using the percentile formula.

  2. Calculate the 90th percentile using the percentile formula.

  3. Subtract the 10th percentile from the 90th percentile.