Question

If xi 's are the midpoints of the class interval of grouped data , fi 's are the corresponding frequencies and x is the mean then find Σ(fixi - x).
(Class 10 Maths Sample Question Paper)

Answer 1

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....

Answer 2

Answer: Zero , 0

Step-by-step 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

HOPE THIS WILL HELP YOU

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