How to Calculate Percentile?

There are different ways by which we can calculate percentile but the basic idea is to find where that number stands if the total no. of observations were 100.

Here are steps by which we can calculate the value at a given percentile in given data.

Step 1 : Arrange Data

Firstly, the data needs to be arranged in an order, preferably increasing order of values.

Step 2 : Calculate Rank

After arranging the data in order, we need to calculate the rank. The formula for rank is given as

Rank = (Desired Percentile/100) × (n+1)

Where n is the number of observations.

Step 3 : Find the Value

• Case 1: If the rank is a whole number, the value at that position in the ordered dataset is the desired percentile.

• Case 2: If the rank is a decimal, interpolate to the nearest whole number to find the percentile value.

Interpolation

Interpolation helps us estimate the exact value when the desired percentile falls between two data points. Here’s how it works:

Identify the Surrounding Data Points: Locate the two data points surrounding the desired percentile.

Calculate the Weighted Average: Take a weighted average of these two data points based on how close the desired percentile is to each point. The closer it is, the more weight it gets.

Calculate the Interpolated Value: To find the interpolated value, we use the formula:

Interpolated Value= Value at Lower Position + (Difference between Higher and Lower Values) × Fractional Rank

Where, “Fractional Rank” is the fractional part of the rank of the desired percentile, indicating its position between the two data points.

Statistics is a polar branch of mathematics that helps us understand data. Ever wondered how well you stack up against others? Percentiles are the key! This article will break down this statistical concept and show you how to find percentiles with ease.