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The sum of standard deviations from the mean is the error.

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the sum of the deviations taken from mean is

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).

zero

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

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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

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

variation

Sum of squares of deviations from the mean is small.

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.

No, a standard deviation or variance does not have a negative sign. The reason for this is that the deviations from the mean are squared in the formula. Deviations are squared to get rid of signs. In Absolute mean deviation, sum of the deviations is taken ignoring the signs, but there is no justification for doing so. (deviations are not squared here)