How to Calculate a Sum of Squared Deviations from the Mean (Sum of Squares)

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A crucial step in many statistical analyses is the calculation of the sum of squared deviations from the mean, sometimes referred to as "calculating the sum of squares" or simply, "calculating the SS." You can plug the result of this calculation into any formula that uses a sum of squares.

  • Calculate the mean (that is, the average) of your list of numbers. This is done simply by adding together all of your numbers, and dividing your result by the total number of numbers on your list.

  • Take the average that you just found, and subtract it from each number on your original list. (This results in a list of many negative numbers, but that's okay!) The list is known as the list of "deviations from the mean."

  • Square each number on your newly modified list of deviations from the mean. (Recall that to "square" a number simply means to multiply it by itself). Because multiplying any number by itself results in a positive number, all the numbers on your resulting list should now be positive. This new list is the list of squared deviations from the mean.

  • Add together all of the numbers on the list of squared deviations from the mean. The result is called "the sum of squared deviations," and can be plugged into any formula that requires a sum of squares (SS) as one of its terms.

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