NIMCET 2017 — Mathematics PYQ

\text{Concept:}  

$\bar{X}=\frac{\sum (f_i{x}_i)}{\sum f_i}$  

\text{Calculation:}  

$\bar{X}=\frac{\sum (f_i{x}_i)}{\sum f_i}$  

$\bar{X}\sum f_i=\sum (f_i{x}_i)\cdots (1)$  

${\sum }_{i=1}^n{f}_i(x_i-\bar{X})=\sum f_i{x}_i-\sum f_i\bar{X}$  

$=\bar{X}\sum f_i-\bar{X}\sum f_i$  

$=0$  

\text{Hence, option (4) is correct.}