How to Calculate Percentile?

How to find Percentile in Statistics?

Percentile Calculation

A Percentile is a measure used in statistics denoting the particular value corresponding to the particular percentage. This measure is used to identify the scores or values falling below or above a particular percentile. For example, the 33^rd percentile refers to the value corresponding to the 33^rd percentage of the list. They are often used in academics to compare student scores. It divides the set of data into 100 equal parts.

The k^th percentile is a value in a data set that splits the data into two pieces. The lower piece contains k percent of the data, and the upper piece contains the rest of the data, that is [100 "“ k] percent. Considering the above said example, the lower piece contains 33 percent of data, and the upper piece contains 67 percentage of data.
Learn how to calculate percentile using this step by step tutorial.

Formula:
To calculate the k^th percentile (where k is any number between zero and one hundred), do the following steps:

1. Arrange the values in the data set in ascending order.
2. Find the "k"^th percentage for the data set. That is, for a data set of 25 numbers, 100% will be 25 and 50% will be 12.5. Similary find the K^th percentage of the data set by multiplying the "k" percent by the total number of values, n.
3. If the number obtained above is not a whole number, round it up to the nearest whole number. This number is called the index and is the number corresponding to the kth percentage.
4. Count the values in the data set from left to right until you reach the index number.
5. Now, the "K^th" percentile is the value corresponding to this index number.

Hence, percentile calculation can be done using the below formula,
K^th Percentile = Value corresponding to the Index Number I
Index Number (I) = K% x N
Where,
N is the total number of values in data set.

Step 1: Assigning Values:
Let us consider a data set with 25 values as given below. We are required to find the 90^th percentile of the data set.
Data Set = 3, 67, 34, 89, 56, 23, 90, 67, 104, 29, 38, 46, 65, 62, 87, 86, 49, 50, 58, 72, 83, 16, 19, 48, 88
N = 25

Step 2: Ordering Data Set
Arrange the numbers in the data set in ascending order.

Data Set (Ordered) = 3, 16, 19, 23, 29, 34, 38, 46, 48, 49, 50, 56, 58, 62, 65, 67, 67, 72, 83, 86, 87, 88, 89, 90, 104

Step 3: Finding Index Number:
Index Number (I) = 90% x 25
= 0.90 x 25
= 22.5
= 23 (Rounded Off)

Step 4: Percentile Calculation
90^th Percentile = Value corresponding to the Index Number (23)
= Value at 23^rd place in data set
= 89

Hence, the 90^th percentile of the given data set is 89, which is the value at the 90^th percentage of the data set, which is the value at the index number 23 out of the total 25 numbers.

Related Topics