Suppose we draw cards from a standard 52 card deck where each card has a value from 1-13 (Ace being 1 King being 13). What is the average deviation of the value of a randomly selected card? What is the average of the sum of 3 randomly selected cards?
The expected value of a given card is 7. Thus average deviation will be $\frac{1(0) + 2(1) + 2(2) + ... + 2(6)}{13} =\frac{42}{13}$. I am assuming average deviation is similar to standard deviation such that for $n$ instances we would scale by $\sqrt{n}$ so average deviation of sum of 3 cards we get $\frac{42\sqrt{3}}{13}$ Is this correct?