Percentile Formula
Percentile Formula is used in determining the performance of a person in comparison with others. It is used mostly in schools during the results of tests to check where a person stands out from others. The percentile formula for a score ‘x’ can be defined as number of scores that fall under ‘x’ divided by the total number of values in the given population.
In this article, we will cover the percentile formula, and some solved examples on it.
What is Percentile?
A percentile is a measure used in statistics to indicate the value below which a given percentage of observations in a group of observations fall.
In simple words, percentiles are a way to express the relative standing of a value within a dataset, indicating what percentage of the data falls below that value. For example, if you scored in the 90th percentile on a standardized test, it means you performed better than 90% of the people who took the test.
What is the Percentile Formula?
The percentile formula is given by:
Percentile(x) = (Number of values fall under ‘x’/total number of values) × 100
P = (n/N) × 100
Where,
- P is percentile
- n – Number of values below ‘x’
- N – Total count of population
The above formula is used to calculate the percentile for a particular value in the population.
If we have percentile value and we need to find the ‘n’ value i.e., for which data value in population then we can rewrite the above formula as-
n = (P × N)/100
Note: First we need to sort the data/population before starting the process.
Also Read,
Sample Problems on Percentile Formula
Question 1: What is percentile value for the score 80 for the given population 50,100,70,80,56,60,80,75.
Solution:
The given data is not sorted. So first sort the data in ascending order.
Sorted data: 50, 56, 60, 70, 75, 80, 80, 100
Number of values fall under 80 (n) = 5
Total count of values (N) = 8
Percentile = (n/N) × 100
= (5/8) × 100
= 62.5
The percentile of value 80 for the given population is 62.5
Question 2: What is the percentile value for the value 60 in a given population of weights of persons 50, 55, 40, 60, 100, 95, 90, 60, 80, 75.
Solution:
The given data is not sorted. So first sort the data in ascending order.
Sorted data: 40,50,55,60,60,75,80,90,95,100
Number of values fall under 60 (n)= 3
Total count of values (N)= 10
Percentile = (n/N) x 100
= (3/10) x 100
= 30
The percentile of value 60 for the given population is 30
Question 3: What is the 15th percentile for the given population of weights of persons 50, 55, 40, 60, 100, 95, 90, 60, 80, 75.
Solution:
The given data is not sorted. So first sort the data in ascending order.
Sorted data: 40,50,55,60,60,75,80,90,95,100
Given, Percentile (P)=15
Total count of values (N)= 10
Need to find n
Percentile = (n/N) x 100
From the given formula we can find n by
n= (P x N)/100
= (15 x 10) / 100
= 150/100
=1.5
1.5 can be rounded off to 2
And 2nd term in the sorted population is 50.
15th percentile value is 50.
Question 4: What is the 50th percentile for the given scores of 8 persons are 50, 100, 70, 80, 56, 60, 80, 75.
Solution:
The given data is not sorted. So first sort the data in ascending order.
Sorted data: 50,56,60,70,75,80,80,100
Given, Percentile (P)=50
Total count of values (N)= 8
Need to find n
Percentile = (n/N) x 100
From the given formula we can find n by
n= (P x N)/100
= (50 x 8) / 100
= 400/100
=4
4th term in the sorted population is 70.
50th percentile value is 70.
Question 5: Find percentile for the value 6 from the given population 1, 6, 7, 3, 8, 9.
Solution:
The given data is not sorted. So first sort the data in ascending order.
Sorted data: 1,3,6,7,8,9
Number of values fall under 6 (n)= 2
Total count of values (N)= 6
Percentile = (n/N) x 100
= (2/6) x 100
= 100/3
= 33.33
The percentile of value 6 for the given population is 33.33
Practice Problems on Percentile Formula
1. Calculate the 40th percentile for the following set of data: {4, 8, 15, 16, 23, 42}
2. Find the 75th percentile for the following set of exam scores: {55, 60, 65, 70, 75, 80, 85, 90, 95, 100}
3. Determine the 90th percentile for the dataset below: {3, 7, 10, 15, 20, 25, 30, 35, 40, 45, 50}.
4. Calculate the 25th percentile for this set of ages: {12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 30}.
FAQs on Percentile
Define Percentile.
A percentile is a statistical measure that indicates the value below which a certain percentage of observations in a dataset or distribution fall.
What is the difference between percentile and percentage?
Percentile indicates the value below which a certain percentage of observations fall in a dataset, while percentage is a measure of a proportion out of 100.
How are percentiles calculated?
Percentiles are calculated by sorting the data in ascending order and then finding the value below which a certain percentage of observations fall. For example, the median is the 50th percentile, meaning 50% of the data falls below it.
How do you interpret percentile rankings?
If you are at the 80th percentile for height, for example, it means you are taller than 80% of the population and shorter than the remaining 20%.
Contact Us