A) 525
B) 380
C) 480
D) 400
Correct Answer: D
Solution :
Mean \[(\mu )=\frac{\sum\limits_{{}}^{{}}{{{x}_{i}}}}{50}=16\] standard deviation\[(\sigma )=\sqrt{\frac{\sum\limits_{{}}^{{}}{x_{i}^{2}}}{50}-{{(\mu )}^{2}}}=16\] \[\Rightarrow (256)\times 2=\frac{\sum\limits_{{}}^{{}}{x_{i}^{2}}}{50}\] \[\Rightarrow \] New mean \[=\frac{\sum\limits_{{}}^{{}}{{{\left( {{x}_{i}}-4 \right)}^{2}}}}{50}=\frac{\sum\limits_{{}}^{{}}{x_{i}^{2}+16\times 50-8\sum\limits_{{}}^{{}}{{{x}_{i}}}}}{50}\] \[=(256)\times 2+16-8\times 16=400\]
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