Statistics And Probability Question 356
Question: The mean of a set of observation is $ \bar{x}. $ if each observation is divided by $ \alpha ,a\ne 0 $ and then is increased by 10, then the mean of the new set is
Options:
A) $ \frac{{\bar{x}}}{a} $
B) $ \frac{\bar{x}+10}{a} $
C) $ \frac{\bar{x}+10a}{a} $
D) $ a\bar{x}+10 $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let $ x_1,x_2….,x_{n} $ be n observations. Then, $ \bar{x}=\frac{1}{n}\Sigma x_{i};Lety_{i}=\frac{x_{i}}{\alpha }+10 $ Then, $ \frac{1}{n}\sum\limits_{i=1}^{n}{y_{i}}=\frac{1}{\alpha }( \frac{1}{n}\sum\limits_{i=1}^{n}{x_{i}} )+\frac{1}{n}(10n) $
$ \Rightarrow \bar{y}=\frac{1}{\alpha }\bar{x}+10=\frac{\bar{x}+10\alpha }{\alpha } $
BETA
