Question

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

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Answer 1

If x_i's are the midpoints of the class intervals of grouped data, f_i's are the corresponding frequencies and ${\displaystyle \overline{x}}$ is the mean, then ${\displaystyle \sum (f_i{x}_i-\overline{x})}$ is equal to 0.

Explanation:-

${\displaystyle \because \overline{x}=\frac{\sum f_i{x}_i}{n}}$

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

${\displaystyle =n\overline{x}-n\overline{x}=0}$