# how does huber compute the $var(s_n)/E[s_n]$ and $var(d_n)/E[d_n]$?

How does Huber in book 'Robust statistical procedures' in chapter 1 compute the variance of certain statistical functions? He defines the mean square deviation to be $$s_n = \sqrt{\frac{1}{n} \sum \left(x_i - \bar{x} \right)^2}$$ and the mean absolute deviation as $$d_n = \frac{1}{n} \sum \| x_i - \bar{x} \|.$$ Then he goes on to obtain the asymptotic relative efficiency expression ARE($$\epsilon$$) as shown in the photo. (So, we should have at least for arguments in the ARE(), namely, ARE($$\epsilon;n,x_i,x$$),right? even if $$n \to \infty.$$ What does ARE() look like before we send $$n \to \infty$$? How on earth does one obtain the expression in the 2nd step?)

What is $$var(s_n), E[s_n]$$? How to obtain these expressions?

Finally, why does he state that just two bad observations in 1000 suffice to offset the 12% advantage of the mean square error? Is is not 5 bad observations? See in the photo, values for $$\epsilon = 0.005$$ is 1.198 which is the (12%) I guess?