Calculating Mean Absolute Deviation (M.A.D.): Step-by-Step Guide and Example

mean absolute deviation (m.a.d.)

Mean absolute deviation (M

Mean absolute deviation (M.A.D.) is a statistical measure that calculates the average absolute difference between each data point in a data set and the mean of that data set. It provides information about the amount of dispersion or variability in the data.

To calculate the mean absolute deviation, follow these steps:

1. Calculate the mean (average) of the data set by summing up all the values and dividing the sum by the number of data points.

2. Find the absolute difference between each data point and the mean by subtracting the mean from each data point and disregarding any negative signs.

3. Sum up all the absolute differences calculated in step 2.

4. Divide the sum of the absolute differences by the number of data points to find the mean absolute deviation.

Here’s an example to illustrate the calculation of M.A.D.:

Consider the following data set: 5, 8, 12, 10, 6

Step 1: Calculate the mean:
Mean = (5 + 8 + 12 + 10 + 6) / 5 = 41 / 5 = 8.2

Step 2: Find the absolute difference between each data point and the mean:
|5 – 8.2| = 3.2
|8 – 8.2| = 0.2
|12 – 8.2| = 3.8
|10 – 8.2| = 1.8
|6 – 8.2| = 2.2

Step 3: Sum up all the absolute differences:
3.2 + 0.2 + 3.8 + 1.8 + 2.2 = 11.2

Step 4: Divide the sum of the absolute differences by the number of data points:
M.A.D. = 11.2 / 5 = 2.24

Therefore, the mean absolute deviation of the given data set is 2.24. This means that, on average, each data point in the set deviates from the mean by approximately 2.24 units.

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