A) \[\sqrt{10}+20\]
B) \[\sqrt{10}+10\]
C) \[\sqrt{10}\]
D) none of these
Correct Answer: C
Solution :
[c] : From the given information, we may write a relation \[y=x+20\], between the two sets of data. [where x denotes the old values and y denotes the new values] So, standard deviation of \[x=\sqrt{10}\] Let \[{{y}_{i}}={{x}_{i}}+20\]where i = 1,2,..., 11 \[\therefore \]\[\overline{y}=\overline{x}+20\] \[\Rightarrow \]\[\frac{1}{n}\sum\limits_{i=1}^{11}{{{({{y}_{i}}-\overline{y})}^{2}}}=\frac{1}{n}\sum\limits_{i=1}^{11}{{{({{x}_{i}}-\overline{x})}^{2}}}\] \[\Rightarrow \]\[\sqrt{\frac{1}{n}\sum\limits_{i=1}^{11}{{{({{y}_{i}}-\overline{y})}^{2}}}}=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{11}{{{({{x}_{i}}-\overline{x})}^{2}}}}=\sqrt{10}\] Thus the standard deviation of y is \[\sqrt{10}\].
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