Statistics And Probability Question 352
Question: The mean of a set of observation is $ \bar{x} $ . If each observation is divided by a, a ¹ 0 and then is increased by 10, then the mean of the new set is
Options:
A) $ \frac{{\bar{x}}}{\alpha } $
B) $ \frac{\bar{x}+10}{\alpha } $
C) $ \frac{\bar{x}+10\alpha }{\alpha } $
D) $ \alpha \bar{x}+10 $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ x_1,x_2 $ ……, $ x_{n} $ be n observations. Then, $ \bar{x}=\frac{1}{n}\Sigma x_{i} $ let $ y_{i}=\frac{x_{i}}{\alpha }+10 $ then, $ \frac{1}{n}\sum\limits_{i=1}^{n}{y_{i}}=\frac{1}{\alpha } $ $ ( \frac{1}{n}\Sigma x_{i} )+\frac{1}{n}(10n) $
Þ $ \bar{y}=\frac{1}{\alpha }\bar{x}+10 $ $ =\frac{\bar{x}+10\alpha }{\alpha } $ .
BETA
