Percentile Rank  

Percentile rank is a statistical measure used to indicate the relative position of a score within a dataset. It shows the percentage of scores that fall below a particular value, helping to understand how well an individual performs compared to others. Commonly used in education, testing, and data analysis, percentile rank provides a clear comparison between scores. 

1.0Percentile Rank Meaning

Percentile rank is a statistical measure that indicates the relative standing of a value within a dataset. It tells us the percentage of scores in the distribution that fall below a particular value.

For example:

If your test score is in the 85th percentile rank, it means you scored better than 85% of the other test-takers.

2.0Difference Between Percentile and Percentile Rank

3.0Percentile Rank Formula

1. Percentile Rank Formula for Ungrouped Data

If the dataset is not categorized into intervals (ungrouped), use this formula:

$\text{Percentile Rank}=\frac{R}{N}\times 100$

Where:

• R = Number of values below the score
• N = Total number of values in the dataset

This gives the percentage of scores less than the given value.

2. Percentile Rank Formula for Grouped Data

When dealing with grouped data (values grouped into class intervals), use this formula:

$\text{Percentile Rank}=\frac{\left(L+\frac{(PN-CF)}{f}\right)-L}{i}\times 100$

Where:

• L = Lower boundary of the percentile class
• P = Desired percentile (as a decimal, e.g., 0.75 for 75th percentile)
• N = Total number of data values
• CF = Cumulative frequency before the percentile class
• f = Frequency of the percentile class
• i = Class interval size

4.0Example of Percentile Rank (Ungrouped Data)

Suppose you have the following scores in a class:

58, 62, 70, 75, 80, 85, 90, 93, 95, 98

You scored 85. How do you find your percentile rank?

Step 1: Count how many values are below 85.

Values below 85: 58, 62, 70, 75, 80 → 5 values

Step 2: Total number of values N = 10

Step 3: Use the formula:

$\text{Percentile Rank}=\frac{5}{10}\times 100=50$

So, your percentile rank is 50.

This means your score is better than 50% of your classmates.

5.0Solved Example on Percentile Rank

Example 1: A class of 50 students took a math test. Rohan scored 82 marks. The number of students who scored less than Rohan is 38. What is the percentile rank of Rohan?

Solution:

The formula for percentile rank is:

$\text{Percentile Rank (PR)}=\left(\frac{\text{Number of values below the score}}{\text{Total number of values}}\right)\times 100$

Step-by-step:

• Number of students below Rohan = 38
• Total students = 50

$PR=\left(\frac{38}{50}\right)\times 100=76$

Answer:

Rohan’s percentile rank is 76.

This means Rohan scored higher than 76% of the students in the class.

Example 2: In a test, Rahul scored better than 42 out of 60 students. What is his percentile rank?

Solution:

$PR=\left(\frac{42}{60}\right)\times 100=70$

Rahul’s percentile rank is 70.

Example 3: Out of 40 students, Priya scored 88 marks. 28 students scored less than her and 3 students scored exactly 88. What is Priya’s percentile rank?

Solution:

For tied scores, use:

$PR=\left(\frac{\text{No. of values below}+0.5\times \text{No. of values equal}}{\text{Total values}}\right)\times 100$ 

$PR=\left(\frac{28+0.5\times 3}{40}\right)\times 100=\left(\frac{29.5}{40}\right)\times 100=73.75$

Priya’s percentile rank is 73.75.

Example 4: A student scores the lowest in a group of 30. What is their percentile rank?

Solution:

No students scored below them.

$PR=\left(\frac{0}{30}\right)\times 100=0$

The percentile rank is 0.

Example 5: In a group of 100 students, Ritu scored the highest. What is her percentile rank?

Solution:

99 students scored below her.

$PR=\left(\frac{99}{100}\right)\times 100=99$

Ritu’s percentile rank is 99.

Example 6: The scores in a class are:

65, 70, 75, 80, 85, 90, 95, 100

Find the percentile rank of the score 85.

Solution:

• Values below 85: 65, 70, 75, 80 → 4 values
• Values equal to 85: 1 value
• Total values: 8

$PR=\left(\frac{4+0.5\times 1}{8}\right)\times 100=\left(\frac{4.5}{8}\right)\times 100=56.25$

Percentile rank of 85 is 56.25.

Example 7: Given the following frequency distribution:

If a student scored 78, find their percentile rank.

Solution:

• Scores below 61–80: 5 + 10 + 8 = 23 students
• Score falls within 61–80, so we estimate position:
• Interval frequency = 12
• 78 is near upper end of the class, so assume approx. 10 out of 12 in the group are below

Total below ≈ 23 + 10 = 33

Total students = 5 + 10 + 8 + 12 + 5 = 40

$PR\approx \left(\frac{33}{40}\right)\times 100=82.5$

Approximate percentile rank is 82.5.

6.0Practice Questions on Percentile Rank

1. In a class of 80 students, Arjun scored better than 60 students. What is his percentile rank?
2. Out of 100 candidates in an exam, 73 scored less than Simran, and 4 scored the same as her. What is Simran’s percentile rank?
3. There are 50 players in a race. A player finishes at 10th position from the top. What is their percentile rank?
4. Given the dataset: 25, 30, 40, 45, 50, 55, 60, 65, 70, 75 Find the percentile rank of the score 55.
5. The frequency table below shows test scores of students:

If a student scores 68, estimate their percentile rank.

6. A student scored the lowest marks in a class of 45. What is the percentile rank of the student?

Answer Key (Short Solutions)

1. PR = (60 / 80) × 100 = 75
2. PR = ((73 + 0.5×4) / 100) × 100 = (75 / 100) × 100 = 75
3. Players below = 40 → PR = (40 / 50) × 100 = 80
4. Below 55: 25, 30, 40, 45, 50 → 5 values

Tied = 1 (55)

PR = ((5 + 0.5×1) / 10) × 100 = 55

5. Below 51–75 range: 4 + 9 = 13

Approx. 9 of 12 in current class are below 68

PR ≈ ((13 + 9) / 30) × 100 = 73.3 (approx)

6. PR = (0 / 45) × 100 = 0

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