I would like to understand the theory behind the standard deviation formula. The way it was explained to me, you have to subtract each value from the mean and square it to avoid the negatives canceling out the positives. After multiplying and dividing by the correct frequencies, we have to square root our sum to correct the effects of squaring it. This explanation doesn't make sense to me because we could have just used absolute values to avoid the positive/negative problem, and it seems more accurate. So why do we use this square and then square root method?