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 :-
Correct Option: , 4
Solution:
Variance is independent of origin. So we shift
the given data by $\frac{1}{2}$.
so, $\frac{10 \mathrm{~d}^{2}+10 \times 0^{2}+10 \mathrm{~d}^{2}}{30}-(0)^{2}=\frac{4}{3}$
$\Rightarrow \mathrm{d}^{2}=2 \Rightarrow|\mathrm{d}|=\sqrt{2}$