English

# How to Calculate Percentile

In statistics, Percentile is used to indicate the value below which the group of percentage of data falls below. For example, consider if your score is 75th percentile, which you scored far better than 75% of people who took part in the test. It is most commonly applicable in indicating the scores from the norm-referenced tests such as SAT, GRE and LSAT. The below percentile example problems provided for your reference in how to calculate percentile with the step by step calculations.

## Percentile Example Problems

Procedure to calculate Kth percentile Step 1: Arrange all data values in the ascending order. Step 2: Count the number of values in the data set where it represented as 'n'. Step 3: Find k /100, where k = any number between zero and one hundred. Step 4: Multiply 'k' percent by 'n'.The resultant number is called as 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 obtained 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.

###### Example 1:

Learn how to calculate percentile for the given example: There are 25 test scores such as: 72,54, 56, 61, 62, 66, 68, 43, 69, 69, 70, 71,77, 78, 79, 85, 87, 88, 89, 93, 95, 96, 98, 99, 99. Find the 60th percentile?

###### Solution:

Step 1: Arrange the data in the ascending order. Ascending Order = 43, 54, 56, 61, 62, 66, 68, 69, 69, 70, 71, 72, 77, 78, 79, 85, 87, 88, 89, 93, 95, 96, 98, 99, 99. Step 2: Find Rank, Rank = Percentile / 100 = 60 / 100 k = 0.60 Step 3: Find 60th percentile, 60th percentile = 0.60 x 25 = 15 Step 4: Count the values in the given data set from left to right until you reach the number 15. From the given data set, 15th number is 79. Now take the 15th number and the 16th number and find the average: 79 + 85 / 2 = 164 / 2 = 82 Hence, 60th percentile of given data set = 82.

###### Example 2:

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

###### Solution:

Step 1: Arrange the data in the ascending order. 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 in the given data set from left to right until you reach the number 10. From the given data set, 10th number is 85.
Hence, 80th percentile of given data set = 85