Introduction

Median absolute deviation (MAD) is a robust statistical measure used to quantify the dispersion or variability of data. It is less sensitive to outliers and extreme values, making it more reliable than standard deviation or variance in certain scenarios. In this article, we will explore how to calculate the median absolute deviation of a dataset.

Step 1: Organize the Data

To begin calculating the MAD, you first need a dataset. Organize your data in ascending order, as this will make it easier to find the median later on.

Dataset example: 3, 4, 6, 8, 9

Step 2: Find the Median

First, identify the center value of your dataset. If there’s an odd number of data points, this is simply the middle value. If there’s an even number of data points, calculate the mean of the two center values.

Dataset example: 3, 4, 6, 8, 9

Median = 6

Step 3: Calculate Absolute Deviations

Next, find the deviations by measuring the difference between each data point and the median identified in Step 2. Remember always to use absolute values, disregarding any negative signs.

Example:

|3-6| = |(-3)| = 3

|4-6| = |(-2)| = 2

|6-6| = |(0)|   = 0

|8-6| = |(2)|   = 2

|9-6| = |(3)|   = 3

Step 4: Find Median of Absolute Deviations

Organize the absolute deviations in ascending order and find their median using a similar approach as in Step 2.

Absolute deviations example:

0, 2, 2, 3, 3

Median Absolute Deviation = 2

Conclusion

In conclusion, the median absolute deviation (MAD) offers an effective way to measure the dispersion of data without being heavily influenced by extreme values or outliers. By following the steps above, you can easily calculate the MAD and fortify your statistical analysis capabilities.