The Essence of Un-Biased Median Absolute Deviation

“ Measuring the variability and spread of data, particularly when robustness to outliers is desired ”

MAD measures the median of the absolute differences between each data point and the overall median of the dataset. This definition might sound complex, but let’s break it down.

MAD is a robust statistic, meaning it’s not easily affect by outliers or extreme values. This makes it particularly useful in scenarios where data may have anomalies.

Lets imagine an example,

Imagine a group of friends standing in a line, each holding a sign with a number on it.

1. Find the middle friend:

• Arrange your friends in order from smallest number to largest number.
• The friend standing exactly in the middle represents the median of the group.

2. Measure the distances to the middle:

• Ask each friend to measure how far away their number is from the middle friend’s number.
• Don’t worry about whether they’re to the left or right, just focus on the distance.
• These distances are called absolute deviations.

3. Find the middle distance:

• Arrange the distances in order, just like you did…