If $x_{i}$ 's are the mid points of the class intervals of grouped data, $f_{1}$ 's are the corresponding frequencies and $¯ x$ is the mean, then $\sum (f_{i} x_{i} - ¯ x)$ is equal to

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Solution

The correct option is A $0$
Given that, $x_{i}$ are the mid points of the class intervals.
$f_{i}$ are the corresponding frequencies.
The mean $¯ x$ for the grouped data is $¯ x = \frac{\sum f_{i} x_{i}}{n}$

$⟹ ¯ x n = \sum f_{i} x_{i}$ ------(1)

$\sum (f_{i} x_{i} - ¯ x) = \sum f_{i} x_{i} - \sum ¯ x$

$⟹ \sum (f_{i} x_{i} - ¯ x) = ¯ x n - \sum ¯ x$ (from (1))

$⟹ \sum (f_{i} x_{i} - ¯ x) = ¯ x n - ¯ x n = 0$

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Similar questions

Q. Question 3
If

x_{i}^{'} s

are the mid-points of the calss intervals of grouped data,

f_{i}^{'} s

are the corresponding frequencies and

¯ x

is the mean, then

\sum (f_{i} x_{i} - ¯ x)

is equal to
(a) 0
(b) -1
(c) 1
(d) 2

If $x_{i}$ are the mid-points of the class intervals of grouped data, $f_{i}$ are the corresponding frequencies and $¯ x$ is the mean, then $\sum f_{i} (x_{i} - ¯ x)$ is equal to ____.

The mid - points of class intervals $x_{i}$ along with respective frequencies $f_{i}$ for recorded observations are given. Calculate the mean deviations about mean $¯ ¯ ¯ x$

Q. If x_i' s are the midpoints of the class intervals of a grouped data, f_i' s are the corresponding frequency and

x

is the mean, then

\sum f_{i} (x_{i} - x) = ?

(a) 1
(b) 0
(c) −1
(d) 2

$i f x_{i}^{'} s a r e t h e m i d p o i n t s o f t h e c l a s s i n t e r v a l s o f a g r o u p e d d a t a, f_{i}^{'} s a r e t h e c o r r e s p o n d i n g f r e q u e n c i e s a n d ¯ x i s t h e m e a n t h e n \sum f_{i} (x_{i} - ¯ x) = ?$

(a) 1 (b) 0 (c) -1 (d) 2

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If xi's are the mid points of the class intervals of grouped data, f1's are the corresponding frequencies and ¯x is the mean, then ∑(fixi−¯x) is equal to

If $x_{i}$ 's are the mid points of the class intervals of grouped data, $f_{1}$ 's are the corresponding frequencies and $¯ x$ is the mean, then $\sum (f_{i} x_{i} - ¯ x)$ is equal to