Question

The mean of a set of observation is $\bar { x }$. If each observation is divided by α, α ≠ 0 and then is increased by 10, then the mean of the new set is

• A. $\frac { \bar { x } } { \alpha }$
• B. $\frac { \bar { x } + 10 } { \alpha }$
• C. $\frac { \bar { x } + 10 \alpha } { \alpha }$
• D. $\alpha \bar { x } + 10$

Answer 1

Answer: (C)

$\frac { \bar { x } + 10 \alpha } { \alpha }$

Answer 2

Let $x _ { 1 } , x _ { 2 }$ ......,$x _ { n }$ be n observations.

Then, let $y _ { i } = \frac { x _ { i } } { \alpha } + 10$

Then, $\frac { 1 } { n } \sum _ { i = 1 } ^ { n } y _ { i } = \frac { 1 } { \alpha }$ $\left( \frac { 1 } { n } \Sigma x _ { i } \right) + \frac { 1 } { n } ( 10 n )$

⇒ $\bar { y } = \frac { 1 } { \alpha } \bar { x } + 10$ $= \frac { \bar { x } + 10 \alpha } { \alpha }$.