What is percentile?
A percentile is a value below which a certain percentage of data falls. It shows the relative standing of a value within a dataset.
If you are in the 90th percentile of a test, it means
- you scored better than 90% of the people who took it or
- you can say that 90% of students are below your score.
What is a Percentage?
A percentage is just a number out of 100. It’s used to express proportions, comparisons, or scores.
If you scored 90% on a test, it means you got 90 out of 100 marks or 9 out of 10 or 18 out of 20 and so on.
Example1:
Let’s say 10 students took a test and got the following scores out of 200:
[30, 60, 180, 170, 120, 140, 150, 160, 100, 90].
Calculate the percentage and percentile of student who scored 120.
ANSWER: Let’s analyze a student who scored 120:
Percentage: Since the test is out of 200, and the student scored 120:
Percentage = (120/200)×100 = 60%
Percentile: First arrange in ascending order:
[30, 60, 90, 100, 120, 140, 150, 160, 170, 180]
Count how many scores are less than 120:
Scores below 120 = [30, 60, 90, 100] → 4 students
Percentile =( 4/10 )×100 = 40th percentile
Even if the students percentage is 60%, his percentile (i.e. 40) depends on how others performed — in this case, better-performing students pushed the percentile down.
Example2:
Let’s say 10 students took a test and got the following scores out of 200:
[30, 60, 180, 170, 120, 140, 150, 160, 100, 90].
Calculate the 30th percentile
ANSWER:
1) First arrange in ascending order:
[30, 60, 90, 100, 120, 140, 150, 160, 170, 180]
2) Calculate the rank (position):
3) Interpolate if necessary
The rank is 3.3, which means the 30th percentile lies between the 3rd and 4th values in the sorted list:
3rd value = 90
4th value = 100
Now interpolate between these two:
30th percentile = 90 + 0.3×(100−90) = 90 + 3 = 93
Interpretation: 30% of students scored below 93.
Example3:
Let's say 10 students took a test and got the following scores out of 200:
[45, 50, 65, 70, 75, 185, 80, 55, 60, 190].
a) Compute percentage and percentile of student who scored 80.
ANSWER: a) Arrange the numbers in ascending:
[45, 50, 55, 60, 65, 70, 75, 80, 185, 190].
Percentage of students who scored 80 = (80/200) * 100 = 40%
Percentile of this student who scored 80 = There are 7 students out of 10 whose scores are below 80:
So percentile of this student is (7/10) * 100 → 70th percentile
Top comments (0)