The mean deviation is squared before being summed otherwise, the deviations would always sum to zero.
The mean deviation is one of the measures of dispersion. We know that the measures of dispersion is a statistical measure of the way that numbers are scattered around the mean of a given number.
We know that it is possible for the mean deviation to be zero. As such, we would need to square it and this is the procedure when we are trying to obtain the mean deviation for any set of values.
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