The outcome of each of 30 items was observed;

Question:

The outcome of each of 30 items was observed;

10 items gave an outcome $\frac{1}{2}-\mathrm{d}$ each, 10 items

gave outcome $\frac{1}{2}$ each and the remaining

10 items gave outcome $\frac{1}{2}+\mathrm{d}$ each. If the

variance of this outcome data is $\frac{4}{3}$ then $|\mathrm{d}|$ equals :-

  1. 2

  2. $\frac{\sqrt{5}}{2}$

  3. $\frac{2}{3}$

  4. $\sqrt{2}$


Correct Option: , 4

Solution:

Variance is independent of origin. So we shift

the given data by $\frac{1}{2}$.

so, $\frac{10 \mathrm{~d}^{2}+10 \times 0^{2}+10 \mathrm{~d}^{2}}{30}-(0)^{2}=\frac{4}{3}$

$\Rightarrow \mathrm{d}^{2}=2 \Rightarrow|\mathrm{d}|=\sqrt{2}$ 

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