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4) The mean absolute deviation of a data set is found by taking the average of the absolute values M of the deviations for each data value in the set. In other words, MAD== 1. Using the weights of M&M; Plain Candies, in grams, from Data Set 27 (27 - M&M; Weights) from the Triola website, are the standard deviation of the weights and the mean absolute deviation of the weights identical? Justify your reasoning. (NOTE: Ignore the separation of data by color. Use the data as a single set.)Explanation / Answer
No, the standard deviation of weights and the mean absolute deviation of weights are not identical. Because, by calculating both, in the excel, we get Std. Deviation = 0.051794, and Mean Absolute Deviation = 0.03703.
Both are different because of the fact that the basic formula of Std. Deviation has a square of deviations from mean, in it, whereas, the formula for Mean absolute deviation has absolute deviation from the mean in it. In the particular dataset of M&M weights, all the observations are less than 1. Hence, squaring and absolute difference, both operations produce significantly different outcomes.
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