Mean Absolute Deviation

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.

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.

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

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

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.

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

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

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

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.

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.