Decile is a statistical measure that divides a dataset into ten equal parts, and each part contains 10% of the data. It is different from percentage as in percentage there are 100 parts. In this article, we will learn in detail about what is decile, the formulas of decile (grouped data and ungrouped data)

What is Decile?

A decile is a quantitative method of dividing data into 10 equal parts. Suppose there is a list of numbers, then the data in the list can be put in order from smallest to largest, and then split into 10 groups with an equal number of numbers in each group. This method is often used in finance and economics studies to help understand and analyze data.

Deciles are different from percentiles, and quintiles quartiles, which divide data into 100 parts, 4 parts, and 5 parts respectively.

Definition of Decile

Splitting a group of data into 10 equal parts is defined as a decile. There are 9 points to divide the data and make sections that each represent 1/10th of the whole. Decile helps arrange a large amount of data in either ascending or descending order.

This arrangement of data is done on a scale of 1 to 10, where each step represents an increase of 10 percentage points.

Formula of Decile

Decile has two ways to be calculated based on the type of data.

Formula of Decile

The two formulas to calculate decile are:

• Decile Formula for Ungrouped Data
• Decile Formula for Grouped Data

Decile Formula for Ungrouped Data

To find the decile for ungrouped data, first, the data needs to be arranged in ascending order. Then, the following formula is applied:

Decile_n = (n/10) × (N + 1)

where,

• Decile_n represents the nth decile.
• n is the decile number (e.g., 1st decile, 2nd decile, etc.).
• N is the total number of data points.

Decile Formula for Grouped Data

To calculate the decile of a grouped data, cumulative frequency is used. The formula to find the decile of a grouped date is as follows:

Decile_n = L + [Tex]\left( \frac{\left(\frac{n}{10} \times N \right) – F}{f} \right) \times c[/Tex]

where,

• Decile_n represents the nth decile.
• n is the decile number (e.g., 1st decile, 2nd decile, etc.).
• L is the lower boundary of the decile class.
• N is the total frequency.
• F is the cumulative frequency of the class preceding the decile class.
• f is the frequency of the decile class.
• c is the class width.

Decile Class Rank

Decile class rank refers to a method of ranking students based on their academic performance relative to their peers within their class. The class is divided into ten equal parts or “deciles,” with each decile representing 10% of the class.

How to Calculate Decile?

Calculate the decile of any given set of data following the steps given below:

Sort the Data: Arrange the data points in ascending order from smallest to largest.

Identify Decile Number: Decide which decile you want to find (e.g., 1st decile, 2nd decile, etc.).

Calculate Position: For ungrouped data, use the formula:

Decile_n = ( n/10 )×(N+1)

Where:

• Decile_n is the nth decile.
• n is the decile number.
• N is the total number of data points.

NOTE: For grouped data, use cumulative frequency to find the position of the decile.

Find the Value: Once you have the position, locate the corresponding value in the sorted data set. This value represents the decile.

Examples of Decile

For example, Suppose we have a data set consisting of the following numbers representing the scores of students in a math test: 65, 72, 84, 57, 68, 75, 80, 92, 88, 78, 60, 70, 85, 95, 62, 73, 79, 83, 90, 77.

Step 1: Arrange the data in increasing order. This gives us: 57, 60, 62, 65, 68, 70, 72, 73, 75, 77, 78, 79, 80, 83, 84, 85, 88, 90, 92, 95.

Step 2: Identify the total number of points. Here, n=20.

Step 3: Apply the decile formula to calculate the position of the required data point.

D(1) = (n+1) / 10 = 21/10 = 2.1

This implies the value of the 2.1st data point has to be determined. This will lie between the scores in the 2nd and 3rd positions. In other words, the 2.1st data point is 0.1 of the way between the scores 60 and 62.

Step 4: The value of the decile can be determined as lower score+(distance)(higher score−lower score). This is given as 60 + 0.1 × (62−60)

= 60 + 0.1 × 2

= 60 + 0.2

= 60.2

Step 5: Apply steps 3 and 4 to determine the rest of the deciles.

D(2) = 2 × (n+1) / 10 = 4.2^th data between digits 4 and 5.

Thus, 62 + 0.2 × (65-62)

= 62 + 0.2 × 3 = 62 + 0.6 = 62.6

Solved Examples on Decile

Example 1: Given the following grouped data representing the scores of students in a class: