The presentation talks about concept, methods of calculation and usages of percentile and percentile rank

1. Percentile and Percentile Rank
Gautam Kumar
Assistant Professor
University Department of Teacher Education
Utkal University, Bhubaneswar

2. PERCENTILE
Introduction:
Percentile (centile) is used to indicate relative position of 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.
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3. PERCENTILE
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 15th percentile, 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.
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4. QUARTILES & DECILES
Quartiles:
A quartiles is the point on the score scale below which a given quarter of the cases lie.
Deciles:
A deciles is the point on the score scale below which a given decile of the cases lie.
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5. QUARTILES & DECILES
Formula for computation of Median
𝑀 𝑑 = 𝐿 +
𝑁
2
− 𝐹
𝑓
x 𝑖
So
1st quartile 𝑄1 = 𝐿 +
𝑁
4
−𝐹
𝑓
x 𝑖
2nd quartile 𝑄2 = 𝐿 +
𝑁
2
−𝐹
𝑓
x 𝑖
3rd quartile 𝑄3 = 𝐿 +
3𝑁
4
−𝐹
𝑓
x 𝑖
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6. QUARTILES & DECILES
Formula for computation of Median
𝑀 𝑑 = 𝐿 +
𝑁
2
− 𝐹
𝑓
x 𝑖
So
1st decile 𝐷1 = 𝐿 +
𝑁
10
−𝐹
𝑓
x 𝑖
5th decile 𝐷5 = 𝐿 +
5𝑁
10
−𝐹
𝑓
x 𝑖
8th quartile 𝐷3 = 𝐿 +
8𝑁
10
−𝐹
𝑓
x 𝑖
and so on
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7. PERCENTILE
Formula for computation of Median
𝑀 𝑑 = 𝐿 +
𝑁
2
− 𝐹
𝑓
x 𝑖
1st percentile 𝑃1 = 𝐿 +
𝑁
100
−𝐹
𝑓
x 𝑖
10th percentile 𝑃10 = 𝐿 +
10𝑁
100
−𝐹
𝑓
x 𝑖
25th percentile 𝑃25 = 𝐿 +
25𝑁
100
−𝐹
𝑓
x 𝑖
50th percentile 𝑃50 = 𝐿 +
50𝑁
100
−𝐹
𝑓
x 𝑖
25th percentile 𝑃75 = 𝐿 +
75𝑁
100
−𝐹
𝑓
x 𝑖
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8. PERCENTILE
General formula for percentile
Percentile, 𝑃 = 𝐿 +
𝑝𝑁
100
−𝐹
𝑓
x 𝑖
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
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9. PERCENTILE
Computation of Quartile, Decile and Percentile
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Scores f
70-79 3
60-69 2
50-59 2
40-49 3
30-39 5
20-29 4
10-19 3
0-9 2
N=24
3rd Quartile 𝑄3 = 𝐿 +
3𝑁
4
−𝐹
𝑓
x 𝑖
Here 3N/4 = 24*3/4 = 18
Here on adding frequencies from below, we find that in the class interval
50-59, quartile 18 will lie
So, L=49.5, F=17, f=2 and i=10
Hence
𝑄3 = 49.5 +
18 − 17
2
x 10

10. PERCENTILE
Computation of Quartile, Decile and Percentile
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Scores f
70-79 3
60-69 2
50-59 2
40-49 3
30-39 5
20-29 4
10-19 3
0-9 2
N=24
25th Percentile
𝑃1 = 𝐿 +
𝑁
100
− 𝐹
𝑓
x 𝑖
24/100 = 0.24

11. PERCENTILE RANK
Percentile Rank:
Percentile rank is the number representing the percentage of the total number of cases
lying below the given scores.
If in a class of 50 students. A student (say student ‘X’) secured a score of 70 on
achievement test. There are 45 other students whose scores falls below the score 70.
Therefore 45 out of 50 (45/50 x 100 = 90%) student lie below the score 45.
Hence, 45 will be termed as 90th percentile of the above data.
The position student ‘X’ enjoys in relation to the other students may be seen by the fact
that the score 45 out of 50 or 90% of the students falls below the score of student ‘X’.
Which means student ‘X’ is better than 90% of students in the calss.
From the above we can conclude that score 70 secured by student ‘X’ has a percentile
rank of 90.
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12. PERCENTILE RANK
Calculation of Percentile from ungrouped data
Scores are
12, 20, 25, 15, 8, 32, 28, 35, 22, 44, 36, 17, 29, 13, 9, 37, 40, 21, 10, 42
What is the percentile rank of 17?
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Scores Rank
44 1
42 2
40 3
37 4
36 5
35 6
32 7
29 8
28 9
25 10
Scores Rank
22 11
21 12
20 13
17 14
15 15
13 16
12 17
10 18
9 19
8 20
Percentile Rank (PR) = 𝟏𝟎𝟎 −
𝟏𝟎𝟎𝑹 −𝟓𝟎
𝑵
Where N = Total no of individual in score group
R = Rank position of the score of an individual whose
percentile rank is to be calculated
𝑷𝑹 = 𝟏𝟎𝟎 −
𝟏𝟎𝟎 ∗ 𝟏𝟒 − 𝟓𝟎
𝟐𝟎
= 32.5 or 32
The percentile rank of the score 17 is 32.

13. PERCENTILE RANK
Calculation of Percentile from grouped data
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Scores Frequency
70-79 3
60-69 2
50-59 2
40-49 3
30-39 5
20-29 4
10-19 3
0-9 2
N=20
First Method
Calculate the percentile rank of score 22
By adding the frequencies from below we see that upto the score
19.5, i.e. the upper limit of the class 10-19, 5 cases lie. Our
requirement here is to find out the number of cases that lie below the
score 22.
Now by observing the frequency distribution, we see that in the class
interval 20-29, 10 scores are shared by 4 individuals.
So, an interval of 10 is shared by 4 individuals, therefore, an interval
of 2.5 is hared by 4/10*2.5=1 individual

14. PERCENTILE RANK
Calculation of Percentile from grouped data
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Scores Frequency
70-79 3
60-69 2
50-59 2
40-49 3
30-39 5
20-29 4
10-19 3
0-9 2
N=20
Therefore, upto the score 22, 5+1 = 6 cases lie
So the required percentile rank is 6*100/24=25

15. PERCENTILE RANK
Calculation of Percentile from grouped data
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Scores Frequency
70-79 3
60-69 2
50-59 2
40-49 3
30-39 5
20-29 4
10-19 3
0-9 2
N=20
Second Method
Calculate the percentile rank of score 22
𝑃𝑅 =
100
𝑁
𝐹 +
𝑋 − 𝐿
𝑖
𝑓
Where:
PR=Percentile rank
F=Cumulative frequency below the interval containing score X
X=Score for which we want to calculate percentile rank
L=Actual lower limit of the interval containing X
i=Size of the class interval
f=Frequency of the interval containing X
N=Total number of cases in the given frequency distribution

16. PERCENTILE RANK
Calculation of Percentile from grouped data
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Scores Frequency
70-79 3
60-69 2
50-59 2
40-49 3
30-39 5
20-29 4
10-19 3
0-9 2
N=20
Here
F=Cumulative frequency below the interval containing score X
L=Actual lower limit of the interval containing X
i=Size of the class interval
f=Frequency of the interval containing X
N=Total number of cases in the given frequency distribution
F=5
X=22
L=19.5
i=10
f=4
N=24
𝑃𝑅 =
100
𝑁
𝐹 +
𝑋 − 𝐿
𝑖
𝑓
= 25

17. USE OF THE PERCENTILE
1. It gives the relative position of the scores.
2. It may be used for comparison such as
a. Two or more students belonging to two or more sections, classes or schools
b. The performance of tow or more classes, sections or schools.
c. The performance of individual if tested under two or more different testing
conditions in terms of possession of some attributes or traits.
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