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.

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

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 k^{th} 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.

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

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:

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

**For 1 ^{st} decile: **

K = 1

n = 10

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

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

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

1^{st} decile = [11 / 10]^{th} data

1^{st} decile = [1.1]^{th} data

1^{st} decile = 1^{st} term + (0.1)^{ th} data

1^{st} decile = 2 + (0.1)^{ th} data

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

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

1^{st} decile = 2 + {(3 – 2) * 0.1}

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

1^{st} decile = 2 + 0.1

1^{st} decile = 2.1

**For 2 ^{nd} decile: **

K = 2

n = 10

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

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

2^{nd} decile = [22 / 10]^{th} data

2^{nd} decile = [2.2]^{th} data

2^{nd} decile = 2^{nd} term + (0.2)^{ th} data

2^{nd} decile = 3 + (0.2)^{ th} data

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

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

2^{nd} decile = 3 + {(4 – 3) * 0.2}

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

2^{nd} decile = 3 + 0.2

2^{nd} decile = 3.2

**For 3 ^{rd} decile: **

K = 3

n = 10

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

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

3^{rd} decile = [33 / 10]^{th} data

3^{rd} decile = [3.3]^{th} data

3^{rd} decile = 3^{rd} term + (0.3)^{ th} data

3^{rd} decile = 4 + (0.3)^{ th} data

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

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

3^{rd} decile = 4 + {(5 – 4) * 0.3}

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

3^{rd} decile = 4 + 0.3

3^{rd} decile = 4.3

**For 4 ^{th} decile: **

K = 4

n = 10

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

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

4^{th} decile = [44 / 10]^{th} data

4^{th} decile = [4.4]^{th} data

4^{th} decile = 4^{th} term + (0.4)^{ th} data

4^{th} decile = 5 + (0.4)^{ th} data

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

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

4^{th} decile = 5 + {(6 – 5) * 0.4}

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

4^{th} decile = 5 + 0.4

4^{th} decile = 5.4

**For 5 ^{th} decile: **

K = 5

n = 10

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

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

5^{th} decile = [55 / 10]^{th} data

5^{th} decile = [5.5]^{th} data

5^{th} decile = 5^{th} term + (0.5)^{ th} data

5^{th} decile = 6 + (0.5)^{ th} data

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

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

5^{th} decile = 6 + {(23 – 6) * 0.5}

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

5^{th} decile = 6 + 8.5

5^{th} decile = 14.5

**For 6 ^{th} decile: **

K = 6

n = 10

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

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

6^{th} decile = [66 / 10]^{th} data

6^{th} decile = [6.6]^{th} data

6^{th} decile = 6^{th} term + (0.6)^{ th} data

6^{th} decile = 23 + (0.6)^{ th} data

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

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

6^{th} decile = 23 + {(32 – 23) * 0.6}

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

6^{th} decile = 23 + 5.4

6^{th} decile = 28.4

**For 7 ^{th} decile: **

K = 7

n = 10

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

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

7^{th} decile = [77 / 10]^{th} data

7^{th} decile = [7.7]^{th} data

7^{th} decile = 7^{th} term + (0.7)^{ th} data

7^{th} decile = 32 + (0.7)^{ th} data

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

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

7^{th} decile = 32 + {(76 – 32) * 0.7}

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

7^{th} decile = 32 + 30.8

7^{th} decile = 62.8

**For 8 ^{th} decile: **

K = 8

n = 10

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

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

8^{th} decile = [88 / 10]^{th} data

8^{th} decile = [8.8]^{th} data

8^{th} decile = 8^{th} term + (0.8)^{ th} data

8^{th} decile = 76 + (0.8)^{ th} data

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

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

8^{th} decile = 76 + {(83 – 76) * 0.8}

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

8^{th} decile = 76 + 5.6

8^{th} decile = 81.6

**For 9 ^{th} decile: **

K = 9

n = 10

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

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

9^{th} decile = [99 / 10]^{th} data

9^{th} decile = [9.9]^{th} data

9^{th} decile = 9^{th} term + (0.9)^{ th} data

9^{th} decile = 83 + (0.9)^{ th} data

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

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

9^{th} decile = 83 + {(91 – 83) * 0.9}

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

9^{th} decile = 83 + 7.2

9^{th} decile = 90.2

**For 10 ^{th} decile: **

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

10^{th} decile = 91

*What are Deciles* | Study.com

*Formula of decile* | WallStreetMojo

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