#### If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and $\bar{x}$  is the mean, then $\Sigma\left(f_{i} x_{i}-\bar{x}\right)$ is equal to (A) 0                (B) –1              (C) 1                (D) 2

Solution.   Mean: It is the average of the given numbers/observations. It is easy to calculate mean. First of all, add up all the observations and then divide by the total number of observations.
That is mean $\left ( \bar{x} \right )= \frac{\sum f_{i}x_{i}}{n}$
By cross multiplication we get

$\sum f_{i}x_{i}= \bar{x}n\cdots (1)$

$\sum \left ( f_{i}x_{i} -\bar{x}\right )= \sum f_{i}x_{i} -\sum \bar{x}$

$= n\bar{x}-\sum \bar{x}$      (from equation (1))
$= n\bar{x}-n\bar{x}$
= 0