Percentile Formula

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

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 percentile is the value below the percentage found from the given data. In our day-to-day life, percentile formulas are usually helpful in finding the test scores or biometric measurements. Hence, the percentile formula is: 

Percentile = (n/N) × 100

Or

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 Formula 

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 

Or 

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

Steps of Percentile Formula 

To find 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: Arrange the data set in ascending order 
• Step 2: Count the number of values in the data set and represent it as r 
• Step 3: Calculate the value of q/100
• Step 4: Multiply q percent by r
• Step 5: If the answer is not a whole number then rounding the number is required. If it is a whole number, continue to the next step
• Step 6: Count the values in the data set, find the mean and the next number. The answer is the qth percentile
• Step 7: Count the value in the data set, once you reach that number according to what we obtained in step 5 that is the qth percentile.

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 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. Find the percentile for the weight 58 kg.

Solution:       

Given: 

Scores obtained by students are 35, 41, 42, 56, 58, 62, 70, 71, 77, 90

Number of people with weight below 58 kg = 4

Using percentile formula,

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 

Rank = 0.07 

Find the percentile using the formula, 

Percentile = Rank × Total number of the data set

Percentile = 0.07 × 10 

Percentile = 0.7 

Since it not a whole number, round the number to the nearest whole number i.e. 0.7 = 1

Count the set to reach the above number. It is 1.

Therefore, the 70th percentile is 45