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Home » If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and x is the mean, then (fixi – ¯¯¯ x ) is equal to (A)0 (B) –1 (C) 1 (D) 2
If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and x is the mean, then (fixi – ¯¯¯ x ) is equal to (A)0 (B) –1 (C) 1 (D) 2
CBSE | Class 10 | Exercise 13.1 | Maths | NCERT Exemplar | Statistics and Probability
If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and x is the mean, then (fixi – ¯¯¯ x ) is equal to (A)0 (B) –1 (C) 1 (D) 2

(A) 0

Clarification:

Mean (x) = Sum of the relative multitude of perceptions/Number of perceptions

    \[x\text{ }=\text{ }\left( f1x1\text{ }+\text{ }f2x2\text{ }+\text{ }\ldots \text{ }..+\text{ }fnxn \right)/f1\text{ }+\text{ }f2\text{ }+\ldots \text{ }\ldots \text{ }+\text{ }fn\]

    \[x\text{ }=\text{ }\Sigma fixi/\Sigma fi,\text{ }\Sigma fi\text{ }=\text{ }n\]

    \[x\text{ }=\text{ }\Sigma fixi/n\]

    \[n\text{ }x\text{ }=\text{ }\Sigma fixi\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }\left( 1 \right)\]

    \[\Sigma \text{ }\left( fixi\text{ }\text{ }x \right)\text{ }=\text{ }\left( f1x1\text{ }\text{ }x \right)\text{ }+\text{ }\left( f2x2\text{ }\text{ }x \right)+\text{ }\ldots \text{ }..+\text{ }\left( fnxn\text{ }\text{ }x \right)\]

    \[\Sigma \text{ }\left( fixi\text{ }\text{ }x \right)\text{ }=\text{ }\left( f1x1\text{ }+\text{ }f2x2\text{ }+\text{ }\ldots \text{ }..+\text{ }fnxn \right)\text{ }\text{ }\left( x\text{ }+x\text{ }+\ldots \text{ }.n\text{ }times \right)\]

    \[\Sigma \text{ }\left( fixi\text{ }\text{ }x \right)\text{ }=\text{ }\Sigma fixi\text{ }\text{ }nx\]

    \[\Sigma \left( fixi\text{ }\text{ }x \right)\text{ }=\text{ }nx\text{ }\text{ }nx\text{ }\left( \text{ }From\text{ }eq1 \right)\]

    \[\Sigma \left( fixi\text{ }\text{ }x \right)\text{ }=\text{ }0\]

Henceforth, choice (A) is right

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