Statistics for People Who (Think They) Hate Statistics

by Neil J. Salkind

sign). Sum the absolute values and divide by the number of data points, and you have the mean deviation. So, if you have a set of scores such as 3, 4, 5, 5, 8 and the arithmetic mean is 5, the mean deviation is the sum of 2 (the absolute value of 5 − 3), 1, 0, 0, and 3, for a total of 6. Then divide this by 5 to get the result of 1.2. (Note: The absolute value of a number is usually represented as that number with a vertical line on each side of it, such as |5|. For example, the absolute value of −6, or |−6|, is 6.) Second, why do we square the deviations? Because we want to get rid of the negative sign so that when we do eventually sum them, they don’t add up to 0. And finally, why do we eventually end up taking the square root of the entire value in Step 7? Because we want to return to the same units with which we originally started. We squared the deviations from the mean in Step 4 (to get rid of negative values) and then took the square root of their total in Step 7 to get back where we started.