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Q: The sum of the deviations from the mean is always?

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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.

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

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

Related questions

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 sum of standard deviations from the mean is the error.

Mean

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

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

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.

The mean.

the mean

Difference (deviation) from the mean.

multiply the mean by the amount of numbers

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.

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