Percentile Formula

The percentile formula determines the performance of a person over others. A percentile is a number that tells the percentage of scores that fall below the given number. Let's discuss this percentile formula in detail and solve a few examples. The percentile is used in finding where a student stands on a test compared to other candidates.

Percentile Definition

The percentile of data value from a set of data values is a statistical measure that gives the percentage of data values that fall below a given data value. For example, in a group of 20 children, Ben is the 4th tallest and 80% of the children are shorter than you. Hence, it means that Ben is at the 80th percentile. It is most commonly used in competitive exams such as SAT, LSAT, etc.

What is Percentile Formula?

The percentile formula is used when we need to compare the exact values or numbers over the other numbers from the given data i.e. the accuracy of the number. Often percentile and percentage are taken as one but both are different concepts. A percentage is where the fraction is considered as one term while a percentile of a value is the percentage of the values that are below the given values out of the whole set of values. The following example will make you understand the meaning and the difference between percentile and percentage. If an exam is conducted out of 100 marks, then:

• we say that a student scored 100 "percent" if and only if he had scored 100/100.
• we say that a student scored 100 "percentile" if all the students (100% students) scored less than him.

Percentile Formula

In our day-to-day life, percentile formulas are usually helpful in grading test scores or biometric measurements. Hence, the percentile formula is:

P = (n/N) × 100

Where,

• n = ordinal rank of the given value or value below the number
• N = number of values in the data set
• P = percentile

The percentile of x is the ratio of the number of values below x to the total number of values multiplied by 100. i.e., the percentile formula is

Percentile = (Number of Values Below “x” / Total Number of Values) × 100

Percentile Calculation

To calculate the percentile, here are a few steps to use the percentile formula. If q is any number between zero and hundred, the qth percentile is a value that divides the data into two parts i.e the lowest part contains the q percent of the data and the rest of the data is the upper part.

• Step 1: Collect the data set
• Step 2: Arrange the data set in ascending order
• Step 3: Determine the total number of observations
• Step 4: Identify the data value for which you are interested to find the percentile
• Step 5: Count the number of data values that are less than the above value
• Step 6: Divide the number from Step 5 by the number from Step 3 to find the percentile of the given data value

☛ Also Check: Percentile Calculator

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Examples Using Percentile Formula

Example 1: The scores obtained by 10 students are 38, 47, 49, 58, 60, 65, 70, 79, 80, 92. Using the percentile formula, calculate the percentile for score 70?

Solution:

Given:

Scores obtained by students are 38, 47, 49, 58, 60, 65, 70, 79, 80, 92

Number of scores below 70 = 6

Using the percentile formula,

Percentile = (Number of Values Below “x” / Total Number of Values) × 100

Percentile of 70

= (6/10) × 100

= 0.6 × 100 = 60

Therefore, the percentile for score 70 = 60%

Example 2: The weights of 10 people were recorded in kg as 35, 41, 42, 56, 58, 62, 70, 71, 90, 77. How to find percentile for the weight 58 kg?

Solution:

Given:

Weight of the people are 35, 41, 42, 56, 58, 62, 70, 71, 77, 90

Number of people with weight below 58 kg = 4

Using the formula for percentile,

Percentile = (Number of Values Below “x” / Total Number of Values) × 100

Percentile for weight 58 kg

= (4/10) × 100

= 0.4 × 100 = 40%

Therefore, the percentile for weight 58 kg = 40%

Example 3: In a college, a list of scores of 10 students is announced. The scores are 56, 45, 69, 78, 72, 94, 82, 80, 63, 59. Using the percentile formula, find the 70th percentile.

Solution: Arrange the data in ascending order - 45, 56, 59, 63, 69, 72, 78, 80, 82, 94

Find the rank,

Rank = Percentile ÷ 100

Rank = 70 ÷ 100 = 0.7

So, the rank is 0.7

Using the formula to calculate the percentile,

Percentile = Rank × Total number of the data set

Percentile = 0.7 × 10

Percentile = 7

Now, counting 7 values from left to right we reach 80, and we can say that all the values below 80 will come under the 70th percentile. In other words, 70% of the values are below 80.

Therefore, the 70th percentile is 80.