Question

Use the definition of the mean to show the sum of the deviation of the observations from their mean is always zero. This is one reason why variance and standard deviation use squared deviations.

Answer 1

Think of the mean as a <I>fulcrum</I> (balance point) of a distribution. To balance, the weights and distances from the fulcrum must be equal, therefore subtracting one side from the other will always = 0 (assuming that you did your calculations correctly).

Answer 2

Sorry for the repeat. However, you need to indicate your subject in the "School Subject" box, so those with expertise in the area will respond to the question. You just lucked out with me responding.