If X̅ is the mean of a distribution of X, then under usual notation \(\displaystyle\sum_{i=1}^n f_i (x_i - \bar{x})\) is?
Concept:
\( \rm \bar x = \frac{\sum ( f_i x_i )}{\sum f_i} \)
Calculation:
\( \rm \bar x = \frac{\sum ( f_i x_i )}{\sum f_i} \)
\( \rm \bar x \sum f_i = \sum ( f_i x_i ) \cdots (1) \)
\( \rm \displaystyle \sum_{i=1}^n f_i (x_i - \bar{x}) = \sum f_i x_i - \sum f_i \bar x \)
= \( \rm \bar x \sum f_i - \rm \bar x \sum f_i \)
= 0
Hence, option (4) is correct.
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