Decile Calculator

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.

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 10^th group of data.

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:

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:

3. So in the ordered dataset, we get:

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 10^th value! We can also see that the 1^st decile rank is equivalent to the 10^th percentile rank!

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

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

We can estimate the 9 deciles using the formula:

Applying this gives us the following results:

If the decile is a fractional or a decimal value, for example, the 2.1^th data in the above dataset, then its calculation would be a little different, and unlike a median calculation. We would calculate the 2.1^th 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 2^nd and 3^rd 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 2^nd data point is -40 + 3.1 = -36.9.
4. Therefore, we get the 1^st decile of the above example dataset as the 2.1^th data point, which is -36.9!

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:

• Normal distribution calculator;
• Geometric distribution calculator;
• Binomial distribution calculator;
• Poisson distribution calculator, etc.

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.

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.

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

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.

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 10^th decile is simply the highest number in the distribution.