Deciles Calculation and Visualization

/ Artificial Intelligence, Data Handling, Deep Learning, Machine Learning, Probability and Statistics, Statistics / By Bindeshwar S. Kushwaha

Hello everyone! Welcome back to Postnetwork Academy. I’m Bindeshwar Singh, and today we’re going to uncover a key concept in statistics that helps you understand data more deeply—deciles!

Have you ever wondered how to break down a data set into smaller, meaningful parts? Deciles allow us to split data into 10 equal sections, giving us a clearer view of its distribution. In this post, we’ll dive into a practical example, learning how to find the 3rd and 7th deciles in an easy, step-by-step way.

Contents hide

1 Deciles Calculation and Visualization

1.1 1. Given Data Set and Decile Calculation

1.2 2. 3rd Decile Calculation

1.3 3. 7th Decile Calculation

1.5 5. Visualization of Data Set with Deciles

1.6 PDF Presentation

Deciles Calculation and Visualization

Author: Bindeshwar

Date: 4/1/2025

1. Given Data Set and Decile Calculation

Given data set: 3, 6, 9, ... , 60

To find the 3rd and 7th deciles, we use the position formula:

$Position of D_{k} = \frac{k \cdot (n + 1)}{10}$

where n = 20.

2. 3rd Decile Calculation

The position of $D_{3}$ :

$Position of D_{3} = \frac{3 \cdot (20 + 1)}{10} = 6.3$

The 3rd decile, $D_{3}$ , is located between the 6th and 7th values (18 and 21):

$D_{3} = 18 + (0.3 \times (21 - 18)) = 18.9$

3. 7th Decile Calculation

The position of $D_{7}$ :

$Position of D_{7} = \frac{7 \cdot (20 + 1)}{10} = 14.7$

The 7th decile, $D_{7}$ , is located between the 14th and 15th values (42 and 45):

$D_{7} = 42 + (0.7 \times (45 - 42)) = 44.1$

4. Results

We conclude that:

3rd Decile ( $D_{3}$ ) = 18.9
7th Decile ( $D_{7}$ ) = 44.1

5. Visualization of Data Set with Deciles

Below is a representation of the number line with the positions of $D_{3}$ and $D_{7}$ marked:

PDF Presentation

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Video

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