question_answer

If \[\overline{\mathbf{x}}\] is the arithmetic mean of n observations \[{{\mathbf{x}}_{\mathbf{1}}},\text{ }{{\mathbf{x}}_{\mathbf{2}}},\text{ }{{\mathbf{x}}_{\mathbf{3}}},\text{ }\ldots \ldots \ldots .,\text{ }{{\mathbf{x}}_{\mathbf{n}}},\]then ________

A) \[\sum\limits_{i=1}^{n}{({{x}_{n}}-\overline{x})}=0\] 

B) \[\sum\limits_{i=1}^{n}{({{x}_{n}}-\overline{x})}=1\]

C) \[\overline{x}=\frac{({{x}_{1}}+{{x}_{2}}+{{x}_{3}}+.....+{{x}_{n}})}{n}\]                       

D) both A and C are correct

E) None of these