Question

If $\overline{x}$ represents the mean of $n$ observations $x_1,x_2,...,x_n$, then value of $\sum _{i=1}^n(x_1-\overline{x})is$ ?

• A. $-1$
• B. $0$
• C. $4$
• D. $n-1$

Answer 1

Answer: (B)

$0$

$\sum _{i=1}^n{x}_i=n\overline{x}$ (given)

$\sum _{i=1}^n(x_i-\overline{x})=\sum _{i=1}^n{x}_i-\overline{x}\sum _{i=1}^{n}1$

$=x\overline{x}-n\overline{x}$

$=0$