A) \[k+s\]
B) s/k
C) ks
D) s
Correct Answer: C
Solution :
[c] Here, \[m=\frac{\Sigma {{x}_{i}}}{5},\,s=\sqrt{\frac{\Sigma x_{i}^{2}}{5}-{{\left( \frac{\Sigma {{x}_{i}}}{5} \right)}^{2}}}\] For observations \[k{{x}_{1}},k{{x}_{2}},k{{x}_{3}},k{{x}_{4}},k{{x}_{5}},\] \[SD=\sqrt{\frac{{{k}^{2}}\Sigma x_{i}^{2}}{5}-{{\left( \frac{k\Sigma {{x}_{i}}}{5} \right)}^{2}}}\] \[=\sqrt{\frac{{{k}^{2}}\Sigma x_{i}^{2}}{5}-{{k}^{2}}{{\left( \frac{\Sigma {{x}_{i}}}{5} \right)}^{2}}}\] \[=k\sqrt{\frac{\Sigma x_{i}^{2}}{5}-{{\left( \frac{\Sigma {{x}_{i}}}{5} \right)}^{2}}}=ks\]
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