A) \[{{\sigma }^{2}}\]
B) \[{{h}^{2}}{{\sigma }^{2}}\]
C) \[h\,{{\sigma }^{2}}\]
D) \[h+{{\sigma }^{2}}\]
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 \[h{{x}_{1}},h{{x}_{2}},...h{{x}_{n}}\] then AM of the values is \[\frac{h{{x}_{1}}+h{{x}_{2}}+...+h{{x}_{n}}}{n}=h\bar{X}\] Therefore, the variance of the new set of values is \[\frac{1}{n}\sum\limits_{i=1}^{n}{(h{{x}_{1}}-h{{\overline{X}}_{2}})={{h}^{2}}\left( \frac{1}{n}\sum\limits_{i=1}^{n}{{{\left( {{x}_{i}}-\bar{X} \right)}^{2}}} \right)={{h}^{2}}{{\sigma }^{2}}}\]
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