The Mean Absolute Deviation (MAD) is a measure of variability used in statistics. It helps determine the spread or dispersion of a data set by calculating the average of the absolute deviations from the mean. MAD is particularly useful for analyzing datasets that contain outlier values, as it is less sensitive to them compared to other measures like variance or standard deviation.

In this article, we will walk you through how to calculate the MAD step by step.

Steps to Calculate Mean Absolute Deviation

1. Calculate the mean of the dataset: To calculate the mean, add up all the data points and divide by the number of items in your dataset.

Mean = Sum of all data points / Number of data points

2. Compute absolute deviations: Subtract the mean value from each data point in your dataset, and then take the absolute value of each difference.

Absolute deviation = |Data point – Mean|

3. Find the sum of absolute deviations: Add up all the absolute deviations from step 2.
Sum of Absolute Deviations = Sum of all |Data point – Mean|

4. Calculate Mean Absolute Deviation: Finally, divide the sum of absolute deviations from step 3 by the number of data points in your dataset.

MAD = (Sum of Absolute Deviations) / Number of data points

Example

Let’s consider a dataset containing five exam scores: 75, 85, 90, 95, and 100.

Step 1: Calculate the mean

Mean = (75 + 85 + 90 + 95 + 100) / 5 = 89

Step 2: Compute absolute deviations

|75 – 89| = 14

|85 – 89| = 4

|90 – 89| = 1

|95 – 89| = 6

|100 – 89| = 11

Step 3: Find the sum of absolute deviations

Sum of Absolute Deviations = 14 + 4 + 1 + 6 + 11 = 36

Step 4: Calculate Mean Absolute Deviation

MAD = 36 / 5 = 7.2

So, the Mean Absolute Deviation for this dataset is 7.2.

Conclusion

Calculating the Mean Absolute Deviation is a straightforward process that allows you to analyze the dispersion of a dataset. By following the steps provided, you can determine how much variation exists within your data. Remember that the MAD is an essential measure in statistics, particularly when examining datasets with outliers or skewed distributions, as it offers a more accurate representation of your data’s variability.