A) 10 or 20
B) 5 or 10
C) 5 or 20
D) 5 or 15
E) 25
Correct Answer: C
Solution :
We know \[SD=\sqrt{\frac{\sum{x_{i}^{2}}}{n}-{{\left( \frac{\sum{{{x}_{i}}}}{n} \right)}^{2}}}\] \[\therefore \]\[2=\sqrt{\frac{100}{n}-{{\left( \frac{20}{n} \right)}^{2}}}=\sqrt{\frac{100}{n}-\frac{400}{{{n}^{2}}}}\] \[\Rightarrow \]\[4=\frac{100}{n}-\frac{400}{{{n}^{2}}}\] \[\Rightarrow \]\[{{n}^{2}}-25n+100=0\]\[\Rightarrow \]\[n=20,5\]
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