Question

The standard deviation of the data:

x:	1	a	a2	.......	an
f:	\(^nC_0\)	\(^nC_1\)	\(^nC_2\)	.......	\(^nC_n\)

Is

A. \(\Big(\frac{1+a^2}{2}\Big)^n-\Big(\frac{1+a}{2}\Big)^n\) 

B.  \(\Big(\frac{1+a^2}{2}\Big)^{2n}-\Big(\frac{1+a}{2}\Big)^n\)

C.  \(\Big(\frac{1+a}{2}\Big)^{2n}-\Big(\frac{1+a^2}{2}\Big)^n\)  

D. none of these

Answer 1

Let us calculate the mean first, 

Mean =  \(\frac{\Sigma f_ix_i}{\Sigma f_i}\)

\(\bar x = \frac{1\times ^nC_0+a\times^nC_1+....+a^n\times^nC_n}{^nC_0+^nC_1+...^nC_n}\) 

\(\bar x = n\Big(\frac{1+a^2}{2}\Big)^{2n}\) 

Standard deviation =  \(\Big(\frac{1+a^2}{2}\Big)^{2n}-\Big(\frac{1+a}{2}\Big)^n\)