Statistics And Probability Question 467
Question: If each observation of a raw data whose variance is $ \sigma $ of the new set is
Options:
A) $ {{\sigma }^{2}} $
B) $ h^{2}{{\sigma }^{2}} $
C) $ h,{{\sigma }^{2}} $
D) $ h+{{\sigma }^{2}} $
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Answer:
Correct Answer: B
Solution:
[b] Let $ x_1,x_2,…x_{n} $ be the raw data. Then, $ {{\sigma }^{2}}=\frac{1}{n}\sum\limits_{i=1}^{n}{{{(x_{i}-\bar{X})}^{2}}} $ If each value is multiplied by h, then values become $ hx_1,hx_2,…hx_{n} $ then AM of the values is $ \frac{hx_1+hx_2+…+hx_{n}}{n}=h\bar{X} $ Therefore, the variance of the new set of values is
$ \frac{1}{n}\sum\limits_{i=1}^{n}(hx_1-h{{\overline{X}} _2})$=
$h^{2}( \frac{1}{n}\sum\limits_{i=1}^{n}{{{( x _{i}-\bar{X} )}^{2}}} )$
=$h^{2}{\sigma }^{2} $
BETA
