Decile Formula

Formula of Decile (Table of Contents)

• Formula
• Example

What is Decile Formula?

In descriptive statistics, the term “decile” refers to the nine values that split the population data into ten equal fragments such that each fragment is representative of 1/10^th of the population. In other words, each successive decile corresponds to an increase of 10% points such that the 1st decile or D₁ has 10% of the observations below it, then 2^nd decile or D₂ has 20% of the observations below it and so on so forth. There are several formulae in vogue to calculate decile, and this method is one of the simplest one where each decile is calculated by adding one to the number of data in the population, then divide the sum by 10 and then finally multiply the result by the rank of the decile i.e. 1 for D₁, 2 for D₂… 9 for D₉.

Mathematically, each decile is represented as,

1^st decile, D₁ = 1 * (n + 1) / 10 th data

2^nd decile, D₂ = 2 * (n + 1) / 10 th data

3^rd decile, D₃ = 3 * (n + 1) / 10 th data

……………………………………

9^th decile, D₉ = 9 * (n + 1) / 10 th data

where n = Number of data in the population or sample

The formula for the i^th decile can be represented as,

Explanation of the Decile Formula

The formula for calculation of decile is derived by using the following steps:

Step 1: Firstly, determine the number of data or variables in the population or sample which is denoted by n.

Step 2: Next, sort the all data or variables in the population in ascending order.

Step 3: Next, based on the decile that is required, determine the value by adding one to the number of data in the population, then divide the sum by 10 and then finally multiply the result by the rank of the decile as shown below.

i^th decile, D_i formula = i * (n + 1) / 10 th data

Step 4: Finally, on the basis of the decile value figure out the corresponding variable from among the data in the population.

Example of Decile Formula (with Excel Template)

Let us suppose that John has been given a set of unsorted data points. He has been asked to sort the number and cut them into 10 equal sections. So, help John do the task of sorting the following 23 random numbers valued from 20 to 78 and presenting then as deciles. The raw numbers are:24, 32, 27, 32, 23, 62, 45, 77, 60, 63, 36, 54, 57, 36, 72, 55, 51, 32, 56, 33, 42, 55, 30.

Given,

• n = 23

Firstly, sort the 23 random numbers in the ascending order like below,

23, 24, 27, 30, 32, 32, 32, 33, 36, 36, 42, 45, 51, 54, 55, 55, 56, 57, 60, 62, 63, 72, 77

So, the calculation of decile can be done as follows-

Similarly, we can calculate each decile as shown above,

Now, D₁ = 1 * (n + 1) / 10 th data = 1 * (23 + 1) / 10

= 2.4^th data i.e. between digit no. 2 and 3

which is = 24 + 0.4 * (27 – 24) = 25.2

Again, D₂ = 2 * (23 + 1) / 10 th data

= 4.8^th data i.e. between digit no. 4 and 5

which is = 30 + 0.8 * (32 – 30) = 31.6

Again, D₃ = 3 * (23 + 1) / 10 th data

= 7.2^th data i.e. between digit no. 7 and 8

which is = 32 + 0.2 * (33 – 32) = 32.2

Again, D₄ = 4 * (23 + 1) / 10 th data

= 9.6^th data i.e. between digit no. 9 and 10

which is = 36 + 0.6 * (36 – 36) = 36

Again, D₅ = 5 * (23 + 1) / 10 th data

= 12^th data i.e. digit no. 12

which is 45

Again, D₆ = 6 * (23 + 1) / 10 th data

= 14.4^th data i.e. between digit no. 14 and 15

which is = 54 + 0.4 * (55 – 54) = 54.4

Again, D₇ = 7 * (23 + 1) / 10 th data

= 16.8^th data i.e. between digit no. 16 and 17

which is = 55 + 0.8 * (56 – 55) = 55.8

Again, D₈ = 8 * (23 + 1) / 10 th data

= 19.2^th data i.e. between digit no. 19 and 20

which is = 60 + 0.2 * (62 – 60) = 60.4

Again, D₉ = 9 * (23 + 1) / 10 th data

= 21.6^th data i.e. between digit no. 21 and 22

which is = 63 + 0.6 * (72 – 63) = 68.4

Decile will be –

Therefore, the deciles value are as follows –

D1 =25.2

Relevance and Uses

It is very important to understand the concept of decile because it is widely used in the field of portfolio management to assess the performance of a portfolio. The decile ranking helps to compare the performance of an asset with other similar assets. decile The decile method is also used by the government to determine the income distribution or level of income equality in a nation. This method of dividing data is used as part of many statistical and academic studies in the fields of economics and finance.

You can download this Decile Formula Excel Template from here – Decile Formula Excel Template

Recommended Articles

This has been a guide to Decile Formula. Here we will learn how to calculate deciles along with some practical examples in Excel and downloadable excel template. You can learn more about financial analysis from the following articles –

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• Formula of Standard Normal Distribution
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