# Decile Calculator

Created by Madhu Raman
Reviewed by Wojciech Sas, PhD candidate and Steven Wooding
Last updated: Jan 18, 2022

The decile calculator helps you split a dataset into different deciles and use the decile scale to compare the data. Much like percentage, percentile and quartile, the decile rank is commonly used in descriptive statistics to divide the data into samples for easier analysis. Using the decile calculation formula, our tool divides the set of observations into 10 samples and allots the decile rank accordingly.

## What does decile mean?

The definition of a decile states that it is the set of 9 values that splits the dataset into 10 groups. It is similar to quartiles and percentiles. Deciles are where the data points are ordered from least to greatest and split into 10 groups with an equal range of values in each. This helps us understand what a decile means.

As a special case, if there are only 9 data points in the set, each of the 9 values will represent the 9 deciles, and there won't be a 10th group of data.

## How do I calculate decile using the decile formula?

To calculate the decile values, we need at least 9 data points in our dataset. We can find the solution for the decile calculation using the following decile formula:

$\footnotesize \ k^{\mathrm{th}}\ \mathrm{decile}\ =\ \left[\frac{k\ \cdot\ (n\ +\ 1)}{10}\right]^{\mathrm{th}}\ \mathrm{data}$

where:

• k = 1, 2, 3, ..., 9; and
• n – Number of data points.

So, for example, if there are 99 data points and we want to know how to calculate decile 1 or the 1st decile, we'll follow these steps:

1. We'd first arrange the values in increasing order to find the decile rank.
2. Use the d1 formula or the formula for the 1st decile:
$\footnotesize\ 1^{\mathrm{st}}\ \mathrm{decile}\ =\ \left[\frac{1\ \cdot\ (99\ +\ 1)}{10}\right]^{\mathrm{th}}\ \mathrm{data}$
1. So in the ordered dataset, we get:
$\footnotesize\quad\ \ \ 1^{\mathrm{st}}\ \mathrm{decile}\ =\ 10^{\mathrm{th}}\ \mathrm{data}$

This way, by using the d1 formula (1st decile formula), we see that for a set of 99 values in the decile scale, the 1st decile will be the 10th value! We can also see that the 1st decile rank is equivalent to the 10th percentile rank!

## Decile calculator solution (example)

Let's say we have the following 20 values in our dataset:

 45 8 -9 10 31 81 -6 -40 0 9 77 54 -43 -2 10 31 0 9 -9 5

First, we'd arrange them in ascending order to get this:

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

-43

-40

-9

-9

-6

-2

0

0

5

8

11th

12th

13th

14th

15th

16th

17th

18th

19th

20th

9

9

10

10

31

31

45

54

77

81

We can estimate the 9 deciles using the formula:

$\quad \footnotesize k^{\mathrm{th}}\ \mathrm{decile}\ =\ \left[\frac{k\ \cdot\ 21}{10}\right]^{\mathrm{th}}\ \mathrm{data}$

Applying this gives us the following results:

1st decile 2nd decile 2.1th data -36.9 4.2th data -8.4 6.3th data -1.4 8.4th data 2 10.5th data 8.5 12.6th data 9.6 14.7th data 24.7 16.8th data 42.2 18.9th data 74.7

If the decile is a fractional or a decimal value, for example, the 2.1th data in the above dataset, then its calculation would be a little different, and unlike a median calculation. We would calculate the 2.1th data point as follows:

1. 2.1 is 0.1 of the distance between 2 and 3, so we will first find the difference between the 2nd and 3rd data points. This will give us -9 - (-40) = 31.
2. We'd then find 0.1 of 31 by multiplying, which would give us 0.1 × 31 = 3.1.
3. 3.1 units from the 2nd data point is -40 + 3.1 = -36.9.
4. Therefore, we get the 1st decile of the above example dataset as the 2.1th data point, which is -36.9!

## Common uses of decile, quartile and percentile

We work with a variety of data in our day-to-day lives and professions. Sometimes, the data that we have may follow a specific kind of distribution, such as:

Even beyond identifying the type of data distribution, we may sometimes want to rank the data on a normalized scale such as test or exam scores, and a few such ranking mechanisms that are most used are:

• Quartiles – to find the top 25% data;
• Deciles – to find the top 10% data; and
• Percentiles – to find the top 1% data.

## FAQ

### What is decile?

The decile definition states that it is a statistical measure that divides a dataset into 10 buckets based on the decile scale. The top decile, for instance, refers to the top (1/10)th of the data values. We can find what the deciles are using the solution to the decile calculation formula. Once we calculate the 9 deciles of the dataset, we can partition the set into 10 segments or ranks.

### Is 90th percentile equivalent to top decile?

The 90th percentile of a dataset is the same as the 9th decile of the same set. Any values above the 90th percentile or the 9th decile will represent the top (1/10)th of the data values. The 10th decile (if it exists) represents the maximum of all the data values.

### How do we calculate quartiles, deciles and percentiles?

Quartiles, deciles, and percentiles are statistical measures used to rank a dataset into different numbers of buckets. To know how to calculate quartiles, deciles, and percentiles, we'd use slightly different formulas, but each of those accomplishes the following:

• Quartiles divide the dataset into 4 ranks;
• Deciles divide the dataset into 10 ranks; and
• Percentiles divide the dataset into 100 ranks.

### What is the tenth decile?

For datasets that have 9 values, we'd have only 9 deciles. But for other datasets that have 10 or more values, we will have 10 deciles, where the 10th decile is simply the highest number in the distribution.

You may enter up to 50 numbers
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
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