Mean absolute deviation (MAD) is a measure of variability that provides information about the spread of data points within a dataset. It indicates how far, on average, the data points are from their mean (average) value. This article will guide you step by step on how to calculate the mean absolute deviation for any dataset.

Step 1: Calculate the Mean

To calculate the mean, you first need to add up all the data points in your dataset and then divide by the number of these data points.

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

Step 2: Calculate the Deviation for Each Data Point

Next, find the deviation for each data point by taking the absolute difference between each data point and the mean.

Deviation = |Data point – Mean|

Step 3: Calculate the Sum of All Deviations

Once you have calculated all deviations for each data point, add up these values to find the sum. Note that because we used absolute values when calculating deviations, all deviations will be positive integers.

Step 4: Calculate the Mean Absolute Deviation

Finally, divide the sum of all deviations by the number of data points in your dataset to find the mean absolute deviation.

Mean Absolute Deviation = (Sum of all deviations) / (Number of data points)

Let’s use an example to further understand these steps:

Example Dataset:

5, 8, 12, 15

Step 1:

Mean = (5 + 8 + 12 + 15) / 4 = 40 / 4 =10

Step 2:

Deviations:

|5 – 10| = |-5|    = 5

|8 – 10| = |-2|    = 2

|12 – 10| = |12-10|=2

|15 – 10| = |5|     =5

Step 3:

Sum of all deviations = 5 + 2 + 2 + 5 = 14

Step 4:

Mean Absolute Deviation = 14 / 4 = 3.5

Thus, the mean absolute deviation of the example dataset is 3.5.

Conclusion:

Calculating mean absolute deviation is a useful way to understand the variability within your dataset, especially when comparing different datasets. By following these four simple steps, you can determine how far, on average, data points are from their mean value, allowing for better decision-making in various analytical and statistical applications.