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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. 

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Decile Calculator


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:

 Decile 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

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