Grade 12th passAlgebra

If the mean of n observations X1, X2,.... Xn is X, then the sum of deviations of observation from mean is 1) 02) nX3) X/n4) none of them

Nikita Singh

8 Years agoGrade 12th pass

Approved Tutor Answer8 Years ago

The question is clear.

Sum of deviations from the mean=(X₁-X)+(X₂-X)+(X₃-X)..............(X_n-X)

= $\sum_{r=1}^{n}(X_{r})-nX$ [ $\because$ X is repeated ‘n’ times]

But from the formula of mean we know that,

$X=\sum_{r=1}^{n}X_{r}/n$

$\sum_{r=1}^{n}X_{r} =nX$

Substituting in the above equation, we get that,

the sum of deviations about mean = nX-nX = 0 (1)

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