A) \[\frac{10}{\sqrt{3}}\]
B) \[\frac{100}{\sqrt{3}}\]
C) \[\frac{100}{3}\]
D) \[\frac{10}{3}\]
Correct Answer: A
Solution :
Let x be the 6th observation \[\Rightarrow 45+54+41+57+43+x=48\times 6=288\] \[\Rightarrow x=48\] variance \[=\left( \frac{\Sigma X_{i}^{2}}{6}-{{(\bar{X})}^{2}} \right)\] \[\Rightarrow \] variance \[=\frac{14024}{6}-{{(48)}^{2}}\]\[=\frac{100}{3}\] \[\Rightarrow \] standard deviation\[=\frac{10}{\sqrt{3}}\]
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