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If $x i$ 's are the mid-points of the class intervals of grouped data, $f i$ 's are the corresponding frequencies and $x ¯$ is the mean, then $f i x i − n x ¯$ is equal to :

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-1

answer is A.

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Detailed Solution

Given that,

x i

's are the mid-points of the class intervals of grouped data,

f i

's are the corresponding frequencies and

x ¯

is the mean
We know,
The formula to find mean through group data is,

x ¯ = ∑ f i x i ∑ f i

The summation sign

Σ

represents the sum of all the terms between given parameters.
Where,

∑ f i = n

. That means

∑ f i

the addition of the total number of terms. Therefore,

x ¯ = f 1 x 1 + f 2 x 2 + f 3 x 3 + … f n x n f 1 + f 2 + f 3 + … . f n ⇒ x ¯ = ∑ f i x i n ⇒ n x ¯ = ∑ f i x i … … (1)

Formulate an equation for the expression

f i x i − n x ¯

We will use summation of ‘n’ number of terms to change the expression

f i x i − n x ¯

From equation (1),

∑ f i x i − x ¯ = n x ¯ − n x ¯ [From equation (1)] ⇒ ∑ f i x i − x ¯ = 0

Therefore,

f i x i − n x ¯ = 0

.
Therefore, option 1 is correct.

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