Question

If x_i' s are the midpoints of the class intervals of a grouped data, f_i' s are the corresponding frequencies and \(\bar{x}\) is the mean then \(\sum{f_i(x_i - x)}\) = ?

(a) 1 

(b) 0 

(c) -1 

(d) 2

Answer 1

Correct answer is (b)0

We know that \(\bar{x}\) = \(\cfrac{\sum f_ix_i}{\sum f_i}\)

⇒ \(\bar{x}\) Σ f_i = Σ f_ix_i … (i) 

Now, Σ f_i (xi − \(\bar{x}\)) = Σ f_ix_i − \(\bar{x}\)Σ f_i 

⇒ Σ f_i (x − \(\bar{x}\)) = Σ f_ix_i − Σ f_ix_i [Using (i)] 

⇒ Σ f_i (x_i − \(\bar{x}\)) = 0