1. Percentage Rank
By: Nikkie G.
Maristela

2. Percentage Rank
 Indicates the percentage of scores that
lies below a given score.
Example, test score which is greater than
95% of the scores of the examinees is
said to be 95th percentile. If the scores
normally distributed, percentile rank can
be inferred from the standard score.

3. In solving Percentile Rank, use the formula:
PR= CF+0.5F X 100
n
where,
PR– percentage rank
CF– cumulative frequency below the given
score
F– frequency of the given score
n– number of scores in the distribution

4. Steps in solving Percentile
Rank
1. Arrange the test scores (TS) from
highest to lowest.
2. Make a frequency distribution of each
score and the number of students
obtaining each score. (F)
3. Find the cumulative frequency (CF) by
adding the frequency in each score
from the bottom upward.
4. Find the percentile rank (PR) in each
score using the formula and the result
as indicated in column 4.

5. Example: the table belowshows the summary of the scores of
the 40 students in a 45 item multiple choice of test. Find the
percentile ranks of the score in the distribution.
TS F TS F
45 1 30 3
43 2 29 4
42 2 28 1
41 1 27 1
25 2
40 1
24 1
39 2
22 2
37 3
21 2
36 2
19 1
34 1
18 2
33 2 16 1
32 2 15 1

6. Find the cumulative frequency of the frequency
distribution. Third column represents the cumulative
property
TS F CF TS F CF
45 1 40 30 3 21
43 2 39 29 4 18
42 2 37 28 1 14
41 1 35 27 1 13
40 1 34 25 2 12
39 2 33 24 1 10
37 3 31 22 2 9
36 2 28 21 2 7
34 1 26 19 1 5
33 2 25 18 2 4
32 2 23 16 1 2
15 1 1
40

7. Find the percentile rank of each score.
a. Solution:
score=45 ; CF=39; F=1; n=40
PR= CF+0.5F X 100
n
PR= 39+0.5(1) X 100
40
PR= 39+0.5 X 100
40
PR=0.9875 X 100
PR= 98.75 or 99
Analysis: A raw score of 45 is equal to
percentile rank of 99. this means that
99% of the students who took examination
had raw scores equal to or lower than

8. 1. Solution:
score=43; CF=37; F=2; n=40
PR= CF+0.5F X 100
n
PR= 37+0.5(2) X 100
40
PR= 37+1 X 100
40
PR=0.95 X 100
PR= 95
Analysis: A raw score of 43 is equal to
percentile rank of 95. This means that 95%
of the students who took examination had
raw scores equal to or lower than 43.

9. 2. Solution:
score=42; CF=35; F=2; n=40
PR= CF+0.5F X 100
n
PR= 35+0.5(2) X 100
40
PR= 35+1 X 100
40
PR=0.9 X 100
PR= 90
Analysis: A raw score of 42 is
equal to percentile rank of 90.
This means that 90% of the
students who took examination
had raw scores equal to or lower
than 42.

10. When converting the raw
scores to a percentile
rank, the raw scores are
put on a scale that has
the same meaning with
different number of
groups and for different
lenghts of tests.

11. Frequency and percentile
ranks distribution of a 45-item
multiple choice of test conducted to
40 studentsPR
TS F CF TS F CF PR
45 1 40 99 29 4 18 40
43 2 39 95 28 1 14 34
42 2 37 90 27 1 13 31
41 1 35 86 25 2 12 28
40 1 34 84 24 1 10 24
39 2 33 80 22 2 9 20
37 3 31 74 21 2 7 15
36 2 28 68 19 1 5 11
34 1 26 64 18 2 4 8
33 2 25 60 16 1 2 4
32 2 23 55 15 1 1 1
30 3 21 49 n=4
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