What is the value of $\Sigma(f_ix_i-\bar x)$?

Question

Let $f_i, \ i=1,2,...n$ be the frequencies of class intervals. Let $x_i, \ i=1,2,...n$ be the class marks. And $\bar x$ is the mean. What is the value of $\Sigma(f_ix_i-\bar x)$?
I got this question in a test. I was confused, whether, a solution even existed or not? Because inserting real values for it, didn't give any constant/fixed value. So, please can anybody point me in the right direction?

Answer 1

Note that $$\bar x=\frac{\sum_\limits{i=1}^{n}x_if_i}{\sum_\limits{i=1}^{n}f_i}$$

So if the summation is from $i=1,2,\cdots n$, then $$\sum (f_ix_i - \bar x)$$ $$=\bar x \cdot \sum_\limits{i=1}^{n}f_i-n \bar x$$ $$=\left(\sum_\limits{i=1}^{n}f_i-n\right)\bar x$$