What does the Mean Absolute Deviation (MAD) represent?

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Multiple Choice

What does the Mean Absolute Deviation (MAD) represent?

Mean Absolute Deviation measures how far, on average, data values are from the center of the data, using absolute distances. It is the average of the absolute deviations from the mean: MAD = (1/n) Σ |x_i − x̄|. This keeps the measure in the same units as the data and shows the typical distance a value is from the mean. For example, with values 3, 5, 7, 9, the mean is 6. The absolute deviations are 3, 1, 1, 3, and the MAD is (3+1+1+3)/4 = 2. This differs from the variance or standard deviation, which involve squaring deviations and are more sensitive to outliers. It’s also not the range (max minus min) or the median. MAD gives a straightforward sense of spread around the center in the original units.

Mean Absolute Deviation measures how far, on average, data values are from the center of the data, using absolute distances. It is the average of the absolute deviations from the mean: MAD = (1/n) Σ |x_i − x̄|. This keeps the measure in the same units as the data and shows the typical distance a value is from the mean.

For example, with values 3, 5, 7, 9, the mean is 6. The absolute deviations are 3, 1, 1, 3, and the MAD is (3+1+1+3)/4 = 2. This differs from the variance or standard deviation, which involve squaring deviations and are more sensitive to outliers. It’s also not the range (max minus min) or the median. MAD gives a straightforward sense of spread around the center in the original units.

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