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
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.
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