Question

If $x_i$'s are the mid points of the class intervals of grouped data, $f_1$'s are the corresponding frequencies and $\overline{x}$ is the mean, then $\sum (f_i{x}_i-\overline{x})$ is equal to

• A. $0$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

Answer: (A)

Given that, $x_i$ are the mid points of the class intervals.

$f_i$ are the corresponding frequencies.

The mean $\overline{x}$ for the grouped data is $\overline{x}=\frac{\sum f_i{x}_i}{n}$

$⟹\overline{x}n=\sum f_i{x}_i$ ------(1)

$\sum (f_i{x}_i-\overline{x})=\sum f_i{x}_i-\sum \overline{x}$

$⟹\sum (f_i{x}_i-\overline{x})=\overline{x}n-\sum \overline{x}$ (from (1))

$⟹\sum (f_i{x}_i-\overline{x})=\overline{x}n-\overline{x}n=0$