---
type: archive
area: archive
status: archived
date: 2026-05-03
created: 2026-05-03
updated: 1980-01-01
tags:
  - archive
---
4.## Median Absolute Deviation (MAD) Calculation

1. **Find the Median (M):**
   Arrange your data in ascending order and find the median.

2. **Calculate Absolute Deviations:**
   Find the absolute difference between each data point and the median.

3. **Find the Median of Absolute Deviations:**
   Calculate the median of these absolute deviations.

**Mathematical Representation:**
\[ MAD = \text{Median}(|X_i - M|) \]

where \( X_i \) is each data point, and \( M \) is the median.

### Example:

Suppose your data set is: 4, 7, 1, 9, 2, 5, 8, 10, 3, 6.

1. **Find the Median (M):**
   Arrange the data in ascending order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
   The median is the average of the 5th and 6th values: \( M = \frac{5 + 6}{2} = 5.5 \).

2. **Calculate Absolute Deviations:**
   |1 - 5.5|, |2 - 5.5|, |3 - 5.5|, |4 - 5.5|, |5 - 5.5|, |6 - 5.5|, |7 - 5.5|, |8 - 5.5|, |9 - 5.5|, |10 - 5.5|

3. **Find the Median of Absolute Deviations:**
   Calculate the median of the absolute deviations.

This median of absolute deviations is the Median Absolute Deviation for your data set. The MAD is a robust measure of dispersion, less sensitive to extreme values compared to the standard deviation.

![[Pasted image 20231221004806.png]]