Percentile Formula, Definition, Examples

Percentile Formula 

Percentile formula is an important math and statistics concept that helps students understand how their score compares to others. It shows the percentage of data points that lie below a particular value. For example, if a student is in the 80th percentile, it means they performed better than 80% of the group.

Knowing the percentile formula enables students to assess exam scores and compare performance objectively. It is used in schools, exams, research, and even health reports. Learning the percentile formula helps students understand relative standing rather than just marks. It also builds confidence and analytical thinking while learning how to study data effectively.

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What is the Percentile Formula?

Percentile formula is used to calculate the relative position of a value in a dataset. It tells what percentage of numbers are smaller than a given value. The percentile definition explains that a percentile divides data into 100 equal parts, each showing a position in the dataset.

The percentile formula is:

Where:

• P = Percentile

• N₍below₎ = Number of values below the given value

• N = Total number of values

For example, if a student ranks 20th among 100 students:

P = (20 / 100) × 100 = 20th percentile

This means the student performed better than 20% of the group.

Read More: Percentage Error

How to Calculate Percentile Using Formula?

Learning how to calculate percentiles using formulas is easy when done step by step. The process helps determine where a value stands in a group or dataset. Follow these simple steps:

Step 1: Arrange the data

Write all the values in ascending order from smallest to largest.

Step 2: Identify the value or rank

Find the value for which you want to calculate the percentile.

Step 3: Apply the formula

Use the percentile formula:

Count how many values are below your chosen value, divide by the total number of values, and multiply by 100.

Step 4: Interpret the result

The result tells the percentage of data that falls below your chosen number.

Another formula used to find the position of a specific percentile is:

Here, Pₖ is the position of the kth percentile in the ordered list. For example, the 25th, 50th, and 75th percentiles divide the data into four equal parts, called quartiles.

This method helps in understanding percentile calculation clearly, whether for test scores or any data analysis.

Read More: Loss Percentage Formula  

Percentile Formula Examples

The following are some simple and clear examples of the percentile formula to help students understand how it works in real-life situations.

Example 1: Exam Scores

Suppose the marks of five students are [50, 60, 70, 80, 90]. To find the 80th percentile:

Total values (N) = 5

Position = (80 / 100) × (5 + 1) = 4.8

The 80th percentile lies between the 4th and 5th scores (80 and 90).

P₈₀ = 80 + 0.8 × (90 - 80) = 88

So, the 80th percentile is 88, which means the student scored better than 80% of the class.

Example 2: Student Rank in Class

If a student ranks 45th out of 50 students:

P = (45 / 50) × 100 = 90th percentile

This means the student performed better than 90% of classmates.

Example 3: Height of Children

In a group of 20 children, a child is taller than 16 others.

P = (16 / 20) × 100 = 80th percentile

So, the child’s height is greater than 80% of the children in the group.

Example 4: Competitive Exam

If a student ranks 150th among 200 candidates:

P = (150 / 200) × 100 = 75th percentile

The student performed better than 75% of the candidates.

Also read: Know Easy Ways to Calculate Profit with Examples

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