What is Decile?

In descriptive statisticsDescriptive StatisticsDescriptive statistics is used to summarize information available in statistics, and there is a descriptive statistics function in Excel as well. This built-in tool is found in the data tab, in the data analysis section.read more, 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.

Decile Formula

There are several formulas in vogue to calculate deciles. 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.

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where n = Number of data in the population or sample

i is the ith decile represents as,

  • 1st decile, D1 = 1 * (n + 1) / 10 th data2nd decile, D2 = 2 * (n + 1) / 10 th data

and so on..

Steps to Calculate Decile

Examples (with Excel Template)

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 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.

  • Firstly, determine the number of data or variables in the population or sample, denoted by n. Next, sort all the data or variables in the population in ascending order. 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. ith decile, Di formula = i * (n + 1) / 10 th data Finally, based on the decile value, figure out the corresponding variable from among the data in the population.

ith decile, Di formula = i * (n + 1) / 10 th data

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

= 2.4th 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

= 4.8th 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

= 7.2th 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

= 9.6th 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

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

which is 45

Again, D6 = 6 * (23 + 1) / 10 th data

= 14.4th 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

= 16.8th 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

= 19.2th 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

= 21.6th 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

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 ranking helps to compare the performance of an asset with other similar assets. The government also uses the decile method 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.

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

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