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Why use standard deviation and not average deviation?
Because the average deviation will always be zero.
How do you find graph median by using standard deviation?
You cannot because the median of a distribution is not related to its standard deviation.
Why normality is required for standard deviation application?
Because the z-score table, which is heavily related to standard deviation, is only applicable to normal distributions.
Why don't all normal curves have the same standard deviation?
Because the standard deviation is one of the two parameters (the other being the mean) which define the Normal curve. The mean defines the location and the standard deviation defines its shape.
Why does the standard deviation weight extreme deviations more than does the arithmetic mean?
Because the standard deviation is based on the square root of the sum of the squares of the deviations, and, as a result, the sum of the squares of the deviations puts more weight in outliers than does a simple arithmetic mean.Note: I wrote this and then had second thoughts, but I'm keeping it in so that someone with more knowledge can weigh in (pun intended). I'm not certain how the arithmetic mean factors into the question. I think the questioner, and definitely this answerer, is confused.
