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The algebraic sum of the deviations of a set of n values from their mean is - Mathematics

MCQ

The algebraic sum of the deviations of a set of n values from their mean is

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  • 0

  • n − 1

  •  n

  • n + 1

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Solution

If `bar( X) `be the mean of the observations q `X_i,...,X_n`, then we have

`bar(X) = 1/nsum_(i=1)^n X_i`

`⇒ sum_(i=1)^n X_i = nbar(X)`

Let ` bar(X)` be the mean of n values `X_i,...,X_n` . So, we have

`bar(X) = 1/nsum_(i=1)^n X_i`

`⇒ sum_(i=1)^n X_i = nbar(X)`

The sum of the deviations of n values `X_i,...,X_n` from their mean`bar(X)` is

`(x_1 - bar(X) ) +(x_2 - bar(X) )+......+(x_n-bar(X))`

`= sum_(i=1)^n(x_i- bar(X))`

`= sum_(i=1)^n x_i- sum_(i=1)^n  bar(X)`

`= nbar(X) - nbar(X)`

=0

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 24 Measures of Central Tendency
Q 12 | Page 22
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