Understanding Mean Absolute Deviation (M.A.D.): Calculation and Interpretation of Data Variability

mean absolute deviation (m.a.d.)

Mean Absolute Deviation (M

Mean Absolute Deviation (M.A.D.) is a measure of the average distance between each data point in a set and the mean of that set. It provides an indication of how spread out the data points are from the mean. M.A.D. is used to assess the variability or dispersion within a dataset.

To calculate the M.A.D., follow these steps:

Step 1: List out the data points in the dataset.

Step 2: Calculate the mean (average) of the dataset by adding up all the data points and then dividing by the total number of data points.

Step 3: Find the absolute deviation for each data point, which is the absolute difference between the data point and the mean. Ignore the negative signs while calculating the absolute differences.

Step 4: Sum up all the absolute deviations obtained in step 3.

Step 5: Divide the sum of the absolute deviations by the total number of data points to find the M.A.D.

Alternatively, you can use the following formula to calculate the M.A.D.:

M.A.D. = Σ|x – mean| / n

Where:
– Σ represents the summation symbol, indicating to sum up all the values.
– |x – mean| represents the absolute difference between each data point (x) and the mean.
– n is the total number of data points in the dataset.

The M.A.D. is to be expressed in the same units as the data points, providing a measure of the average absolute dispersion from the mean.

For example, let’s consider the dataset: 4, 6, 8, 10, 12.

Step 1: List out the data points: 4, 6, 8, 10, 12.

Step 2: Calculate the mean: (4 + 6 + 8 + 10 + 12) / 5 = 8.

Step 3: Find the absolute deviation for each data point:
|4 – 8| = 4
|6 – 8| = 2
|8 – 8| = 0
|10 – 8| = 2
|12 – 8| = 4

Step 4: Sum up all the absolute deviations: 4 + 2 + 0 + 2 + 4 = 12.

Step 5: Divide the sum of the absolute deviations by the total number of data points: 12 / 5 = 2.4.

Therefore, the Mean Absolute Deviation (M.A.D.) for the given dataset is 2.4. This indicates, on average, the data points deviate from the mean by a value of 2.4.

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