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# Decile Calculator

## How to use this decile calculator?

To use the decile calculator, you have to follow the below steps:
• Enter the comma-separated values (minimum 9 terms)
• Click on the “calculate” button
• If you want to erase the input, click the “reset” button.

## Decile calculator:

The decile calculator calculates the deciles (1st to 10th) of the entered data set it also calculates the minimum value, maximum value, mean, sum, and range of the given input.

## What are deciles?

In statistics, deciles are a measure of position that divides a dataset into 10 equal parts, each containing an equal number of observations.

Specifically, the kth decile is the value below which k/10 of the observations in the dataset fall, and above which (10 - k) / 10 of the observations fall. It is quite similar to quartiles

• The first decile (10th percentile) is the value below which 10% of the observations in the dataset fall
• The second decile (20th percentile) is the value below which 20% of the observations fall.
• The fifth decile (50th percentile) is the value below which 50% of the observations fall, which is also known as the median.

## Formulas for calculating the deciles of a data set:

To calculate the decile of a data set we use the following formula: • “K” is the number of deciles it can be between 1 to 10
• “n” is the number of terms

## Example section:

In this section, we’ll discuss the steps for calculating the deciles of any data set.

Example 1:

Calculate the deciles of the following data set:

2, 23, 4, 91, 5, 6, 3, 76, 83, 32

Solution:

Step 1: Arrange the data

Firstly we have to arrange the data in ascending order.

X = 2, 3, 4, 5, 6, 23, 32, 76, 83, 91

Step 2: Calculate “n”.

Total number of terms = n = 10

Step 3: Calculation.

Calculate the deciles using the formula:

Kth decile = [{k * (n + 1)} / 10]th data

For 1st decile:

K = 1

n = 10

Kth decile = [{k * (n + 1)} / 10]th data

1st decile = [{1 * (10 + 1)} / 10]th data

1st decile = [{1 * (11)} / 10]th data

1st decile = [11 / 10]th data

1st decile = [1.1]th data

1st decile = 1st term + (0.1) th data

1st decile = 2 + (0.1) th data

For “(0.1)th data” subtract 1st term from the 2nd term, and then multiply it by “0.1”

1st decile = 2 + {(2nd term – 1st term) * 0.1}

1st decile = 2 + {(3 – 2) * 0.1}

1st decile = 2 + {(1) * 0.1}

1st decile = 2 + 0.1

1st decile = 2.1

For 2nd decile:

K = 2

n = 10

2nd decile = [{2 * (10 + 1)} / 10]th data

2nd decile = [{2 * (11)} / 10]th data

2nd decile = [22 / 10]th data

2nd decile = [2.2]th data

2nd decile = 2nd term + (0.2) th data

2nd decile = 3 + (0.2) th data

For “(0.2) th data” subtract 2nd term from the 3rd term, and then multiply it by “0.2”

2nd decile = 3 + {(3rd term – 2nd term) * 0.2}

2nd decile = 3 + {(4 – 3) * 0.2}

2nd decile = 3 + {(1) * 0.2}

2nd decile = 3 + 0.2

2nd decile = 3.2

For 3rd decile:

K = 3

n = 10

3rd decile = [{3 * (10 + 1)} / 10]th data

3rd decile = [{3 * (11)} / 10]th data

3rd decile = [33 / 10]th data

3rd decile = [3.3]th data

3rd decile = 3rd term + (0.3) th data

3rd decile = 4 + (0.3) th data

For “(0.3) th data” subtract 3rd term from the 4th term, and then multiply it by “0.3”

3rd decile = 4 + {(4th term – 3rd term) * 0.3}

3rd decile = 4 + {(5 – 4) * 0.3}

3rd decile = 4 + {(1) * 0.3}

3rd decile = 4 + 0.3

3rd decile = 4.3

For 4th decile:

K = 4

n = 10

4th decile = [{4 * (10 + 1)} / 10]th data

4th decile = [{4 * (11)} / 10]th data

4th decile = [44 / 10]th data

4th decile = [4.4]th data

4th decile = 4th term + (0.4) th data

4th decile = 5 + (0.4) th data

For “(0.4) th data” subtract 4th term from the 5th term, and then multiply it by “0.4”

4th decile = 5 + {(5th term – 4th term) * 0.4}

4th decile = 5 + {(6 – 5) * 0.4}

4th decile = 5 + {(1) * 0.4}

4th decile = 5 + 0.4

4th decile = 5.4

For 5th decile:

K = 5

n = 10

5th decile = [{5 * (10 + 1)} / 10]th data

5th decile = [{5 * (11)} / 10]th data

5th decile = [55 / 10]th data

5th decile = [5.5]th data

5th decile = 5th term + (0.5) th data

5th decile = 6 + (0.5) th data

For “(0.5) th data” subtract 5th term from the 6th term, and then multiply it by “0.5”

5th decile = 6 + {(6th term – 5th term) * 0.5}

5th decile = 6 + {(23 – 6) * 0.5}

5th decile = 6 + {(17) * 0.5}

5th decile = 6 + 8.5

5th decile = 14.5

For 6th decile:

K = 6

n = 10

6th decile = [{6 * (10 + 1)} / 10]th data

6th decile = [{6 * (11)} / 10]th data

6th decile = [66 / 10]th data

6th decile = [6.6]th data

6th decile = 6th term + (0.6) th data

6th decile = 23 + (0.6) th data

For “(0.6) th data” subtract 7th term from the 6th term, and then multiply it by “0.6”

6th decile = 23 + {(7th term – 6th term) * 0.6}

6th decile = 23 + {(32 – 23) * 0.6}

6th decile = 23 + {(9) * 0.6}

6th decile = 23 + 5.4

6th decile = 28.4

For 7th decile:

K = 7

n = 10

7th decile = [{7 * (10 + 1)} / 10]th data

7th decile = [{7 * (11)} / 10]th data

7th decile = [77 / 10]th data

7th decile = [7.7]th data

7th decile = 7th term + (0.7) th data

7th decile = 32 + (0.7) th data

For “(0.7) th data” subtract 7th term from the 8th term, and then multiply it by “0.7”

7th decile = 32 + {(7th term – 6th term) * 0.7}

7th decile = 32 + {(76 – 32) * 0.7}

7th decile = 32 + {(44) * 0.7}

7th decile = 32 + 30.8

7th decile = 62.8

For 8th decile:

K = 8

n = 10

8th decile = [{8 * (10 + 1)} / 10]th data

8th decile = [{8 * (11)} / 10]th data

8th decile = [88 / 10]th data

8th decile = [8.8]th data

8th decile = 8th term + (0.8) th data

8th decile = 76 + (0.8) th data

For “(0.8) th data” subtract 8th term from the 9th term, and then multiply it by “0.8”

8th decile = 76 + {(9th term – 8th term) * 0.8}

8th decile = 76 + {(83 – 76) * 0.8}

8th decile = 76 + {(7) * 0.8}

8th decile = 76 + 5.6

8th decile = 81.6

For 9th decile:

K = 9

n = 10

9th decile = [{9 * (10 + 1)} / 10]th data

9th decile = [{9 * (11)} / 10]th data

9th decile = [99 / 10]th data

9th decile = [9.9]th data

9th decile = 9th term + (0.9) th data

9th decile = 83 + (0.9) th data

For “(0.9) th data” subtract 9th term from the 10th term, and then multiply it by “0.9”

9th decile = 83 + {(10th term – 9th term) * 0.9}

9th decile = 83 + {(91 – 83) * 0.9}

9th decile = 83 + {(8) * 0.9}

9th decile = 83 + 7.2

9th decile = 90.2

For 10th decile:

The maximum term of the data set is the 10th decile, so:

10th decile = 91

## References:

What are Deciles | Study.com

Formula of decile | WallStreetMojo