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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.

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Q: When computing the sample variance the sum of squared deviations about the mean is used for what reason?

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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)

ABSURDITY

to organize similar data

You need a job at the end of it?

For the same reason that numbers in ordinary notation need computing.

With the advent of Cloud Computing, there is no more reason for you computing for individual users can be hosted in a professional data center instead of on a desk.

A favorable/unfavorable price variance does not effect your quantity variance. The reason you would see a favorable price variance and an unfavorable quantity variance is because you consumed more materials than your standard allows AND the price you paid for those material was less than your standard price. If you paid more than your standard price, you would have experienced an unfavorable variance in both quantity and price.

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

Generally not without further reason. Extreme values are often called outliers. Eliminating unusually high values will lower the standard deviation. You may want to calculate standard deviations with and without the extreme values to identify their impact on calculations. See related link for additional discussion.

for profit.........

In my point of view The First reason is to study the mobile computing history is the very nature of the application may require the use of a communication network that connects several computers.

Cubed. The reason is that space has three dimensions - and that is basically what we are measuring.

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