Question 3
If $x_{i}^{'} s$ are the mid-points of the calss intervals of grouped data, $f_{i}^{'} s$ are the corresponding frequencies and $¯ x$ is the mean, then $\sum (f_{i} x_{i} - ¯ x)$ is equal to
(a) 0
(b) -1
(c) 1
(d) 2

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Solution

$∵ ¯ x = \frac{\sum f_{i} x_{i}}{n} ∴ \sum (f_{i} x_{i} - ¯ x) = s u m f_{i} x_{i} - \sum ¯ x = n ¯ x - n ¯ x [∵ s u m ¯ x = n ¯ x] = 0$

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