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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)

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

Grade:11

1 Answers

Arun
25763 Points
2 years ago
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
HOPE THIS WILL HELP YOU....
 
 

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