Question

Mean of 'n' items is $\overline{x}$. If these n items are successively increased by $2,2^2,2^3$,.... $2^n$, then the new mean is?

• A. $\overline{x}+\frac{2^{n+1}}{n}$
• B. $\overline{x}+\frac{2^{n+1}}{n}-\frac{2}{n}$
• C. $\overline{x}+\frac{2^n}{n}$
• D. $\overline{x}+2^n$

Answer 1

Answer: (B)

$\overline{x}+\frac{2^{n+1}}{n}-\frac{2}{n}$

$\left(\frac{x_1+x_2+........+x_n}{n}\right)=\overline{x}newmean\left(\frac{(x_2+2)+(x_2+2^2)+............+(x_n+2^n)}{n}\right)=\left(\frac{x_1+x_2+........+x_n}{n}\right)+\left(\frac{2+2^2+........+2^n}{n}\right)=\overline{x}+2\times \left(\right(\frac{1-2^n}{1-2}\left)\right)\times \left(\frac{1}{n}\right)=\overline{x}+\left(\frac{2^{n+1}-2}{n}\right)=\overline{x}+\frac{2^{n+1}}{n}-\left(\frac{2}{n}\right)$