Decile Formula

Decile Formula (Table of Contents)

• Formula
• Examples

What is Decile Formula?

Decile, as its name sounds, is a statistical term which divides the data into ten defined intervals. It basically divides the data points into a data set in 10 equal parts on the number line. This type of data ranking is used in many fields like finance and economics etc. One thing we need to keep in mind is that data points can be random and we have to put those number in line first on the number line in ascending order and then divide them in deciles. Once we divide the data, decile ranking can be given:

Like other tools quartile and percentile, decile is also a method which divides data into smaller parts which are easier to measure, analyze and understand.

Formula For Decile:

Let’s say that we have a data set with N data points:

X – {X1, X2, X3……….. XN}

Formula for Deciles is given by:

D1 = (N+1) * 1 / 10

D2 = (N+1) * 2 / 10

And so on till

D9 = (N+1) * 9 / 10

From the above formula, we can see D5 = (N+1) * 5 /10 = (N+1)/2 which is the median. So 5^th decile represents the median.

For grouped data:

Where:

i = 1, 2, 3, 4, 5…, 9

• L – Lower boundary of a group
• h – Width
• f – frequency
• N – Total number of data points
• C – Cumulative frequency preceding to that class

Examples of Decile Formula (With Excel Template)

Let’s take an example to understand the calculation of Decile in a better manner.

Decile Formula – Example #1

Let’s say we have a data sets which contains 39 data points. Calculate the Deciles.

Data Set:

Solution:

First of all, we have to arrange this in ascending order i.e. from lowest to highest.

Decile is calculated using the formula given below

D_i = (N + 1) * i / 10

The result will be as given below.

Similarly, calculate for all the points.

Now

• D1 = (39 + 1) * 1 / 10 = 40 / 10 = 4^th data point = 10
• D2 = (39 + 1) * 2 / 10 = 80 / 10 = 8^th data point = 17
• D3 = (39 + 1) * 3 / 10 = 120 / 10 = 12^th data point = 38
• D4 = (39 + 1) * 4 / 10 = 160 / 10 = 16^th data point = 49
• D5 = (39 + 1) * 5 / 10 = 200 / 10 = 20^th data point = 58
• D6 = (39 + 1) * 6 / 10 = 240 / 10 = 24^th data point = 64
• D7 = (39 + 1) * 7 / 10 = 280 / 10 = 28^th data point = 73
• D8 = (39 + 1) * 8 / 10 = 320 / 10 = 32^th data point = 84
• D9 = (39 + 1) * 9 / 10 = 360 / 10 = 36^th data point = 91

If you see the data set, the median of this set is: (n + 1)/2 = 40 / 2 = 20^th value i.e. 58, this is same as D5.

Decile Formula – Example #2

Suppose below is the given frequency table you have with you for which you need to calculate the deciles.

From the above image, we have given the following information.

Decile is calculated using the formula given below

Di = L + (h / f) * (I * (N / 10) – C)

The result will be as given below

Similarly, calculate for other values

Di = L + (h / f) * (i * (N / 10) – C)

• D1 = 10 + (10 / 8) * (1 * (70 / 10) – 0) = 18.75
• D2 = 20 + (10 / 12) * (2 * (70 / 10) – 8) = 25
• D3 = 30 + (10 / 14) * (3 * (70 / 10) – 20) = 30.7
• D4 = 40 + (10 / 10) * (4 * (70 / 10) – 34) = 34
• D5 = 50 + (10 / 6) * (5 * (70 / 10) – 44) = 35
• D6 = 60 + (10 / 16) * (6 * (70 / 10) – 50) = 55
• D7 = 70 + (10 / 4) * (7 * (70 / 10) – 66) = 27.5

Explanation

We know that quartiles divides data into four equal groups, a decile divides data into ten equal parts Decile, as discussed above gives ranks to a data set from lowest to highest. This is done on the scale of 1 to 10 where each number basically indicates an increase of 10 percentage points. So 1st decile has 10% of the data points below it, D2 has 20% of the data points below it and so on. So Decile rankings is another method to categorize data like quartile or percentile.

Relevance and Uses of Decile Formula

As discussed above, Decile helps us in dividing the data into ten parts very quickly and eventually makes it easy for us to understand the data in these parts. In finance, deciles are used to analyze the performance of different funds by ranking them and measuring the performance of one fund against similar funds. For example, you are an analyst and evaluating a set of mutual funds, so any fund which is ranked 6 on a decile scale, it means that it is in the top 60% of the funds. So basically we can use deciles and can segregate these funds into best and worst-performing funds for a particular period.

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