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Byju's Answer

Standard X

Mathematics

Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

If xi's are...

Question

If $x i$ 's are the mid-point of the class intervals of a grouped data, $f i^{'} s$ are the corresponding frequencies and $¯ x$ is the mean, then find $\sum (f i (x i - ¯ x)$ .

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Solution

We know that, $x_{i}$ are the known as class marks of the class interval and thus it an be used to find Mean in the following way,
$\Rightarrow ¯ x = \frac{\sum f i x i}{\sum f i}$
$∴ \sum f i x i = ¯ x \sum f i$ ....(i)
Now,
$\sum f i (x i - ¯ x)$
$= \sum f i x i - \sum f i ¯ x$
$= \sum f i ¯ x - \sum f i ¯ x$ [From (i)]
$= 0$

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Similar questions

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

Q. Question 3
If

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

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Q. If

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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 ____.

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If xi's are the mid-point of the class intervals of a grouped data, fi′s are the corresponding frequencies and ¯x is the mean, then find ∑(fi(xi−¯x).

We know that, xi are the known as class marks of the class interval and thus it an be used to find Mean in the following way,⇒¯x=∑fixi∑fi∴∑fixi=¯x∑fi ....(i)Now,∑fi(xi−¯x)=∑fixi−∑fi¯x=∑fi¯x−∑fi¯x [From (i)]=0

If $x i$ 's are the mid-point of the class intervals of a grouped data, $f i^{'} s$ are the corresponding frequencies and $¯ x$ is the mean, then find $\sum (f i (x i - ¯ x)$ .