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+1 vote
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in Statistics by (47.3k points)
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If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and x is the mean, then (fixi – \(\overline x\) ) is equal to

(A) 0 (B) –1 (C) 1 (D) 2

1 Answer

+2 votes
by (48.7k points)
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Best answer

(A) 0

Explanation:

Mean (x) = Sum of all the observations/ Number of observations

x = (f1x1 + f2x2 + …..+ fnxn) / f1 + f2 +……+ fn

x = Σfixi / Σfi, Σfi = n

x = Σfixi / n

n x = Σfixi …………… (1)

Σ (fixi – x) = (f1x1 – x) + (f2x2 – x)+ …..+ (fnxn – x)

Σ (fixi – x) = (f1x1 + f2x2 + …..+ fnxn) – (x +x +….n times)

Σ (fixi – x) = Σfixi –nx

Σ(fixi – x) = nx – nx ( From eq1)

Σ(fixi – x) = 0

Hence, option (A) is correct

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