how to find the mean absolute deviation

Daniel Parker

2 min read

·

17-03-2025

1

0

Share

The mean absolute deviation (MAD) is a simple way to measure how spread out a set of data is. It tells us, on average, how far each data point is from the mean (average) of the dataset. Understanding how to calculate MAD can be useful in various fields, from statistics to finance. This guide will walk you through the process step-by-step.

Understanding the Mean Absolute Deviation

Before diving into the calculation, let's clarify what the MAD represents. It's a measure of variability or dispersion. A small MAD indicates that the data points are clustered closely around the mean, while a large MAD suggests a greater spread. Unlike variance or standard deviation, MAD uses the absolute values of the differences, avoiding the complications of negative values cancelling out positive ones.

Steps to Calculate the Mean Absolute Deviation

Here's a breakdown of how to calculate the MAD, illustrated with an example:

Example Dataset: Let's use the following dataset representing the daily temperatures (in Celsius) for a week: 20, 22, 25, 23, 21, 24, 26

Step 1: Calculate the Mean

First, find the mean (average) of the dataset. Add all the values together and divide by the number of values.

• 20 + 22 + 25 + 23 + 21 + 24 + 26 = 161
• 161 / 7 = 23

The mean temperature is 23°C.

Step 2: Find the Absolute Deviations

Next, find the absolute difference between each data point and the mean. "Absolute difference" simply means the positive difference; ignore any negative signs.

• |20 - 23| = 3
• |22 - 23| = 1
• |25 - 23| = 2
• |23 - 23| = 0
• |21 - 23| = 2
• |24 - 23| = 1
• |26 - 23| = 3

Step 3: Calculate the Mean of the Absolute Deviations

Finally, calculate the mean of these absolute deviations. Add up all the absolute deviations and divide by the number of values.

• 3 + 1 + 2 + 0 + 2 + 1 + 3 = 12
• 12 / 7 ≈ 1.71

Therefore, the mean absolute deviation (MAD) for this dataset is approximately 1.71°C. This means that, on average, the daily temperatures deviated by about 1.71°C from the mean temperature of 23°C.

Why Use Mean Absolute Deviation?

• Easy to Understand and Calculate: MAD is straightforward and requires only basic arithmetic.
• Robust to Outliers: While sensitive to outliers, it's less sensitive than variance or standard deviation. Outliers can significantly inflate variance and standard deviation.
• Intuitive Interpretation: The MAD directly represents the average distance from the mean, providing a clear picture of data dispersion.

Mean Absolute Deviation vs. Standard Deviation

While both MAD and standard deviation measure dispersion, they differ in their calculation methods. Standard deviation squares the deviations before averaging, making it more sensitive to outliers. MAD uses absolute values, offering a more robust measure in the presence of extreme values. The choice between the two depends on the specific data and the desired level of sensitivity to outliers.

Applications of Mean Absolute Deviation

The mean absolute deviation finds applications in various fields:

• Finance: Assessing the volatility of investment returns.
• Quality Control: Monitoring the consistency of a manufacturing process.
• Meteorology: Analyzing the variability of weather patterns.
• Healthcare: Studying the variability of patient outcomes.

Understanding and calculating the mean absolute deviation is a valuable skill in interpreting and analyzing data. Its simplicity and intuitive interpretation make it a useful tool for various applications. Remember to choose the measure of dispersion (MAD or Standard Deviation) that best suits your needs and data characteristics.