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Q: What is the sum of the deviations from the mean?

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The sum of total deviations about the mean is the total variance. * * * * * No it is not - that is the sum of their SQUARES. The sum of the deviations is always zero.

Zero.

0 (zero).

multiply the mean by the amount of numbers

zero

Mean

The definition of the mean x of a set of data is the sum of all the values divided by the total number of observations, and this value is in turn subtracted from each x value to calculate the deviations. When the deviations from the average are added up, the sum will always be zero because of the negative signs in the sum of deviations. Going back to the definition of the mean, the equation provided (x = Σxi/n) can be manipulated to read Σxi - x = 0

Sum of squares of deviations from the mean is small.

variation

The sum of deviations from the mean, for any set of numbers, is always zero. For this reason it is quite useless.

You want some measure of how the observations are spread about the mean. If you used the deviations their sum would be zero which would provide no useful information. You could use absolute deviations instead. The sum of squared deviations turns out to have some useful statistical properties including a relatively simple way of calculating it. For example, the Gaussian (or Normal) distribution is completely defined by its mean and variance.

For which measure of central tendency will the sum of the deviations always be zero?

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