Mean Absolute Deviation

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What is Mean Absolute Deviation (M.A.D.)?

Back

Mean Absolute Deviation (M.A.D.) is a measure of the dispersion or spread of a set of data points. It represents the average distance between each data point and the mean of the data set.

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How do you calculate the Mean Absolute Deviation?

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1. Find the mean of the data set. 2. Subtract the mean from each data point and take the absolute value of each result. 3. Find the average of these absolute values.

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What does a lower M.A.D. indicate about a data set?

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A lower M.A.D. indicates that the data points are closer to the mean, suggesting more consistency in the data.

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What does a higher M.A.D. indicate about a data set?

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A higher M.A.D. indicates that the data points are more spread out from the mean, suggesting greater variability in the data.

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Given the data set 9, 7, 11, 10, 8, what is the M.A.D.?

Back

1. Mean = 9. 2. Absolute deviations: |9-9|, |7-9|, |11-9|, |10-9|, |8-9| = 0, 2, 2, 1, 1. 3. M.A.D. = (0+2+2+1+1)/5 = 1.2.

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If the M.A.D. of a data set is 0, what does that mean?

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If the M.A.D. is 0, it means all data points are identical and equal to the mean.

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What is the significance of M.A.D. in real-world applications?

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M.A.D. helps in understanding the reliability and consistency of data, which is crucial in fields like finance, quality control, and research.

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How can M.A.D. be used to compare two data sets?

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By comparing the M.A.D. of two data sets, one can determine which set has more variability or consistency.

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What is the M.A.D. of the ages: 11, 34, 16, 18, 22, 30, 18, 20, 15, 16?

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1. Mean = 19. 2. Absolute deviations: |11-19|, |34-19|, |16-19|, |18-19|, |22-19|, |30-19|, |18-19|, |20-19|, |15-19|, |16-19| = 8, 15, 3, 1, 3, 11, 1, 1, 4, 3. 3. M.A.D. = (8+15+3+1+3+11+1+1+4+3)/10 = 5.2.

Front

What is the M.A.D. of the data set 58, 38, 54, 48, 20, 26, 36?

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1. Mean = 38. 2. Absolute deviations: |58-38|, |38-38|, |54-38|, |48-38|, |20-38|, |26-38|, |36-38| = 20, 0, 16, 10, 18, 12, 2. 3. M.A.D. = (20+0+16+10+18+12+2)/7 = 11.42.