Percentiles are used to indicate the relative position of a score in a group of scores. They divide the scores into 100 equal parts. The 50th percentile, also called the median, is the score below which 50% of scores fall. Percentiles are calculated using a formula that determines the value of the observation corresponding to the percentile rank based on the total number of observations. For example, the 10th percentile is the score below which 10% of scores fall. Percentiles are useful for comparing individual test scores to the overall score distribution.

1. By
Dr. Abhishek Srivastava
Percentile

2. I 2
• Introduction:
• Percentile (centile) is used to indicate
relative positionof a single item or an
individual with reference to the group to which the item or individual
belongs.
• It denotes the relative position of given score among other score.
PERCENTILE

3. I 3
Definition:
• Percentile is a point on a score scale below which a given percent of cases lie.
It is denoted by Pn , where n is the number of percentile.
• P1 is first percentile, which means it is a point on the given score below which 1%
score lies. Means 99% score are above this point.
• P15 is 15thpercentile, which means it is a point on the given score below which
15% score lies. Means 85% score are above this point.
• P50 is 50th percentile, which means it is a point on the given score below which
50% score lies. Means 50% score are above this point. It is also know as Median.
PERCENTILE
I

4. Percentiles are the values of arranged data which divide whole data
into hundred equal parts. They are 9 in numbers namely P1,P2,⋯,P99.
Here P1 is first percentile, P2 is second percentile, P3 is third percentile
and so on.
Formula
• The formula for ith percentile is
• Pi= Value of (i(n+1)/100)th observation, i=1,2,3,⋯,99
• where n is the total number of observations.
Percentiles for ungrouped data

5. • The test score of a sample of 20 students in a class are as follows:
• 20,30,21,29,10,17,18,15,27,25,16,15,19,22,13,17,14,18,12 and 9.
• Find the value of P10, P20 and P80.
Solution
• The sample size is n=20.
• The formula for ith percentile is
• Pi= Value of (i(n+1)/100)th observation, i=1,2,3,⋯,99
• where n is the total number of observations.
• Arrange the data in ascending order
• 9, 10, 12, 13, 14, 15, 15, 16, 17, 17, 18, 18, 19, 20, 21, 22, 25, 27, 29, 30
• Tenth percentile P10
• The tenth percentile P10 can be computed as follows:
Example

7. PERCENTILE
General formula for percentile
𝑝 𝑁
−𝐹
I 7
I
100
𝑓
x 𝑖Percentile, 𝑃 = 𝐿 +
Where
L=Lower limit of the percentile class (the class in which the given percentile may be
suppose to lie)
N=Total number of frequencies
F=Total number of frequencies before percentile class
f=Frequency of percentile class
i=Size of the class interval
p=No. of percentile which has to be computed

8. PERCENTILE
I 8
f PERCENTILE
1st percentile 𝑃1= 𝐿 +
𝑁
−𝐹
100
𝑓
x 𝑖
10th percentile 𝑃10 = 𝐿+
10𝑁
−𝐹
100
𝑓
x 𝑖
25th percentile 𝑃25 = 𝐿 +
25𝑁
−𝐹
I
100
𝑓
x 𝑖
50th percentile 𝑃50 = 𝐿 +
50𝑁
−𝐹
100
𝑓
x 𝑖
x 𝑖

9. PERCENTILE
IGAUTAM 9
Computation of Percentile 25th PercentileScores f cF
70-79 3 24
60-69 2 21
50-59 2 19
40-49 3 17
30-39 5 14
20-29 4 9
10-19 3 5
0-9 2 2
N=24
Thursday, 30 July 2020 UUDTE I UTKAL UNIVERSITY
Px =pN/100
P25=24x25/100
=6
L=19.5
CF=5
i =10
N=24
f =4

10.  P25= 19.5+ (25x24/100- 5)x10/4
 P25= 19.5+ (6- 5)x10/4
 P25= 19.5+ (1)x10/4
 P25= 19.5+2.5
 P25= 22

11. THANKS