Decile

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 1/10th of the population. In other words, each successive decile corresponds to an increase of 10% points that the 1st decile or D1 has 10% of the observations below it. Then, the 2nd decile, or D2, has 20% of the observations below it, and so on.

It arranges the data from the lowest to the highest form and each successive value shows an increase of 10%. It is a method to catagorize the numerical data. It is widely used in economics and finance but should be used only after arranging the data in ascending order.

Decile rank is a quantitative process of dividing a set of data into tenequal parts. For this purpose, it is necessary to arrange the data systematically in ascending order. It is widely used for statistical study in the economics and finance field.

The primary purpose of the process is to make the data more valuable and easy to comprehend and analyze. First, the analysts try to find the lowest and highest values using this method. Then, ranks are assigned to the data, showing a 10% rise in each successive data. So, there will be nine points in the distribution.

There are several formulas in vogue to calculate decile. This method is one of the simplest ones where one can calculate each decile by adding one to the number of data in the population, then dividing the sum by ten, and then finally multiplying the result by the rank of the decile, i.e., 1 for D1, 2 for D2… 9 for D9.

D_i = i * (n + 1) / 10 th data

where n = Number of data in the population or sample

i is the ith decile rank represents as,

• 1^st decile, D₁ = 1 * (n + 1) / 10 th data
• 2^nd decile, D₂ = 2 * (n + 1) / 10 th data

and so on..

Let us follow the below steps to calculate decile.

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

    

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

    

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

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

4. Finally, based on the decile value, figure out the corresponding variable from among the data in the population.

    

Let us suppose that John has given a set of unsorted data points. He has asked to sort the numbers and cut them into 10 equal sections. So, help John sort the following 23 random numbers valued from 20 to 78 and present them as decile grouped data. 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 can be 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

The decile will be:

Therefore, the value is as follows –

D1 =25.2

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

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

Decile in statistics divides a set of data into 10 parts and percentile divides a set of data into 100 parts. But let us look at the differences between them in details.