If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and \bar{x}  is the mean, then \Sigma\left(f_{i} x_{i}-\bar{x}\right) is equal to
(A) 0                (B) –1              (C) 1                (D) 2

Answers (1)

Answer. [A]

Solution.   Mean: It is the average of the given numbers/observations. It is easy to calculate mean. First of all, add up all the observations and then divide by the total number of observations.
That is mean \left ( \bar{x} \right )= \frac{\sum f_{i}x_{i}}{n}
  By cross multiplication we get

\sum f_{i}x_{i}= \bar{x}n\cdots (1)

\sum \left ( f_{i}x_{i} -\bar{x}\right )= \sum f_{i}x_{i} -\sum \bar{x}

                = n\bar{x}-\sum \bar{x}      (from equation (1))
              = n\bar{x}-n\bar{x}
               = 0      

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