A) \[\frac{\overline{x}}{m}+n\]
B) \[\frac{\overline{x}}{n}+m\]
C) \[\overline{x}+\frac{n}{m}\]
D) \[\overline{x}+\frac{m}{n}\]
Correct Answer: A
Solution :
Let the observations be \[{{x}_{1}},{{x}_{2}},{{x}_{3}}.....{{x}_{r}}\] \[\Rightarrow \] \[\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+....+{{x}_{t}}}{t}=\bar{x}\] Now, if each observation is divided by m and increased by n, then the new observations are \[\frac{{{x}_{1}}}{m}+n,\,\,\frac{{{x}_{2}}}{m}+n......\frac{{{x}_{t}}}{m}+n\] \[\therefore \] Mean of new observations \[=\frac{\frac{{{x}_{1}}}{m}+n+\frac{{{x}_{2}}}{m}+n+.....+\frac{{{x}_{t}}}{m}+n}{t}\] \[=\frac{\frac{1}{m}\,({{x}_{1}}+{{x}_{2}}+....+{{x}_{t}})+n\times t}{t}=\frac{{\bar{x}}}{m}+n\]
You need to login to perform this action.
You will be redirected in
3 sec
