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multiply the mean by the amount of numbers

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Q: How do you calculate the sum of the deviations from the mean?

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standard deviation is the positive square root of mean of the deviations from an arithmatic mean X denoted as sigma.sigma=sqrt {(sum(x-X)^2)/n}

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.

You calculate the mean.For each observation, you calculate its deviation from the mean.Convert the deviation to absolute deviation.Calculate the mean of these absolute deviations.

No. It cannot be. Remember that when you square a negative number it becomes a positive number. Thus all squared deviations are positive and their sum must be positive.

The sum will be zero or close to zero, depending on how the sampling was done. See related question.

Related questions

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

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.

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

Zero.

0 (zero).

zero

Mean

standard deviation is the positive square root of mean of the deviations from an arithmatic mean X denoted as sigma.sigma=sqrt {(sum(x-X)^2)/n}

Square the standard deviations, subtract/add them and calculate the square root of the subtraction/sum. StDV=sqrt (StDvA^2+StDvB^2)

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.