Question

If mean of $x_1,x_2,x_3...........x_{20}$ is $25$, then $\stackrel{20}{\sum _{i=1}}(x_1-25)=?$

• A. $20$
• B. $0$
• C. $25$
• D. None of these

Answer 1

Answer: (B)

$0$

$x_1,x_2,x_3,.........x_{20}$

Total no. od terms $=20$

Mean $\left(\overline{x}\right)$ of the given data-

$\overline{x}=\frac{{\sum }_{i=1}^{20}{x}_i}{20}$

Given that mean of given data is $25$.

$\therefore \frac{{\sum }_{i=1}^{20}{x}_i}{20}=25$

$\Rightarrow {\sum }_{i=1}^{20}{x}_i=25\times 20$

Now,

${\sum }_{i=1}^{20}(x_i-25)$

$={\sum }_{i=1}^{20}{x}_i-{\sum }_{i=1}^{20}25$

$=(25\times 20)-(20\times 25)$

$=0$

Hence the value of ${\sum }_{i=1}^{20}(x_i-25)$ is $0$.