Upper Bounds on Deviations from the Mean and the Mean Absolute Deviation

چکیده مقاله

In this paper, a number of upper bounds are introduced for the mean absolute deviation (MAD) from the mean when there is some information about the number of the data that are above or below the average. The upper bounds are compared with each other according to their tightness. A unified structure is found to be useful to prove all of the proposed upper bounds as well as the other existing upper bounds. In the path to formulate that structure, also, an upper bound is introduced for the individual deviations from the mean. The results are clarified and verified by a few examples.