If x_i are the mid ponts of a class interval of a grouped data & f_i are the corresponding frequencies & x bar is the mean , then find ∑f_i (x_i – x bar)

Solution:
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

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