Measurement : Understanding Quartiles and IQRs

Quartiles and Interquartile Range (IQR) are ways of measuring the distribution of data.

Quartiles

A quartile is a value that divides a set of data into four equal groups. The first quartile (Q1) is the value that separates the bottom 25% of the data from the top 75%. The second quartile (Q2) is the median, which is the value that separates the bottom 50% of the data from the top 50%. The third quartile (Q3) is the value that separates the bottom 75% of the data from the top 25%.

Interquartile Range (IQR)

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It is a measure of how spread out the middle 50% of the data is. A larger IQR indicates that the data is more spread out, while a smaller IQR indicates that the data is more tightly clustered together.

Lets imagine

You have a group of 100 students and you want to know how tall they are. You collect the height of each student and arrange the data from shortest to tallest. The median height would be the height of the 50th student. Q1 would be the height of the 25th student, and Q3 would be the height of the 75th student. The IQR would be the difference between Q3 and Q1.

In general, a larger IQR means that the data is more spread out, while a smaller IQR means that the data is more tightly clustered together. However, it is important to note that the IQR is not a measure of the total spread of the data. It only takes into account the middle 50% of the data.

Example:

Data: [100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000]

Lets solve it using python

In conclusion, quartiles and IQRs are fundamental tools for understanding and analyzing the distribution of data. They provide valuable insights into the spread and variability of data, making them essential for descriptive statistics, outlier detection, and data analysis across various fields.

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