The outcome of each of 30 items was observed; 10 items gave an outcome [1 2] -- d each, 10…

Question

The outcome of each of 30 items was observed; 10 items gave an outcome $${1 \over 2}$$ -- d each, 10 items gave outcome $${1 \over 2}$$ each and the remaining 10 items gave outcome $${1 \over 2}$$+ d each. If the variance of this outcome data is $${4 \over 3}$$ then |d| equals :

Accepted Answer

Variance is independent of region. So we shift the given data by $${1 \over 2}$$.

so,   $${{10{d^2} + 10 \times {0^2} + 10{d^2}} \over {30}} - {\left( 0 \right)^2} = {4 \over 3}$$

$$ \Rightarrow $$  d2 $=$ 2 $$ \Rightarrow $$ $$\left| d \right| = \sqrt 2 $$

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