A percentile is a statistical measure that indicates the value below which a given percentage of observations in a group of data falls. It helps understand how a particular value compares to the rest of the data.
- 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.
It is commonly used in schools to understand how well someone did on a test compared to everyone else. The percentile of a score 'x' is calculated by dividing the number of scores below 'x' by the total number of scores. It tells us the value below which a specific percentage of data points fall in a given dataset.
To find the value corresponding to a specific percentile, the following formula is used:
Percentile(x) = (Number of values fall under 'x'/total number of values) × 100
P = (n/N) × 100
Where,
- P is the 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 a percentile value and we need to find the 'n' value, i.e., for which data value in the 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.
Solved Question on Percentile Formula
Question 1: What is the 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
= 62.5The 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 person A, percentile 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) = 10Percentile = (n/N) x 100
= (3/10) x 100
=30The 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) = 10Need 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 2And 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, 100Given, Percentile (P) = 50
Total count of values (N) = 8Need to find n
Percentile = (n/N) x 100From the given formula we can find n by
n= (P x N)/100
= (50 x 8) / 100
= 400/100
=44th term in the sorted population is 70.
50th percentile value is 70.
Question 5: Find the 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, 9Number of values fall under 6 (n) = 2
Total count of values (N) = 6Percentile = (n/N) x 100
= (2/6) x 100
= 100/3
= 33.33The percentile of value 6 for the given population is 33.33
Unsolved Questions on the Percentile Formula
Question 1: Calculate the 40th percentile for the following set of data: {4, 8, 15, 16, 23, 42}.
Question 2: Find the 75th percentile for the following set of exam scores: {55, 60, 65, 70, 75, 80, 85, 90, 95, 100}.
Question 3: Determine the 90th percentile for the dataset below: {3, 7, 10, 15, 20, 25, 30, 35, 40, 45, 50}.
Question 4: Calculate the 25th percentile for this set of ages: {12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 30}.
Answer:
- 13.6.
- 91.25.
- 49.
- 15.