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If x¯ is the mean of n values of x, then ∑i=1n(xi-x¯) is always equal to ______. If a has any value other than x¯, then ∑i=1n(xi-x¯)2 is ______ than ∑(xi-a)2 - Mathematics

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Question

If `barx` is the mean of n values of x, then `sum_(i = 1)^n (x_i - barx)` is always equal to ______. If a has any value other than `barx`, then `sum_(i = 1)^n (x_i - barx)^2` is ______ than `sum(x_i - a)^2`

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Solution

If `barx` is the mean of n values of x, then `sum_(i = 1)^n (x_i - barx)` is always equal to 0. If a has any value other than `barx`, then `sum_(i = 1)^n (x_i - barx)^2` is less than `sum(x_i - a)^2`

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Chapter 15: Statistics - Exercise [Page 283]

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NCERT Exemplar Mathematics [English] Class 11
Chapter 15 Statistics
Exercise | Q 41 | Page 283

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