A) 5
B) \[\sqrt{5}\]
C) \[\sqrt{7}\]
D) 2
Correct Answer: B
Solution :
| \[\sum{{{({{x}_{i}}+1)}^{2}}=9n}\] | ? (i) |
| \[\sum{{{({{x}_{i}}-1)}^{2}}=5n}\] | ? (2) |
| (1)+(2) \[\Rightarrow \]\[\sum{(x_{i}^{2}+1)=7n}\] | |
| \[\Rightarrow \] \[\frac{\sum{x{}_{i}^{2}}}{n}=6\] | |
| (1) . (2) \[\Rightarrow \]\[4\sum{{{x}_{i}}=4n}\] | |
| \[\Rightarrow \] \[\sum{{{x}_{i}}=n}\] |
| \[\Rightarrow \] \[\frac{\sum{{{x}_{i}}}}{n}=1\] |
| \[\Rightarrow \] variance \[=6-1=5\] |
| \[\Rightarrow \] standard deviation \[=\sqrt{5}.\] |
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