Quartiles and its Uses

In this class, We discuss Quartiles and its Uses.

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The reader should have prior knowledge of the measure of central tendency. Click Here.

Quartiles:

Quartiles are three points that divide the data series into four equal parts.

Example:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Total, we have n observations.

n = 12 in our example

Q1, Q2, and Q3 are quartile points.

The three points, Q1, Q2, and Q3, divide the data into four equal parts.

Q1 is our first quartile point.

25% of the data is left of the quartile value.

Q2 is our second quartile.

50% of the data is left in the quartile Q2.

Q2 is called the median quartile.

Q1 is called the lower quartile.

Q3 is called the upper quartile.

Q1 = ((n +1)/4)th observation

Q2 = ((n +1)/2)th observation

Q3 = (3(n +1)/4)th observation

Use of quartile points

Simply finding the measure of central tendency will not help much in data analysis.

The quartile points help in a deeper understanding of data.

Example: Marks in a class

45, 46, 47, 48, 52, 55, 59, 62, 68, 69

The quartiles help to identify poor students and good students

Quartile points in a symmetric distribution

The below diagram shows the symmetric distribution

Quartiles and its Uses 1
Symmetric Distribution

This graphical intuition helps readers to understand the next classes.

Quartiles in asymmetric distribution.

The below diagram shows the asymmetric distribution.

Quartiles and its Uses 2
Asymmetric Distribution

The data before the lower quartile are below the poverty line.

The data after the upper quartile are rich.