Answer to Question #164608 in Statistics and Probability for Kamrul

Question

MD=SD=R/2 (Sign are natural)

Answer 1

Without going to the $\dfrac{R\text{(Range)}}{2}$ part,

 Why do you think $MD = SD$ ?

That is NOT generally true (although data can be constructed such that MD = SD).

For example: $x = {[-10, 0, 10]}, SD(x) = \sqrt{\dfrac{(10^2 + 0 + 10^2)}{3}} = ~2.72$

(or another answer if you divide by $N-1$ instead of $N$ )

 $MD(x) = \dfrac{(10 + 0 + 10)}{3} = 6.66...$

$SD(x) \neq MD(x)$

Hence, $MD\neq SD\neq \dfrac{R}{2}$