Question

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

• A. $2$
• B. $\frac{\sqrt{5}}{2}$
• C. $\frac{2}{3}$
• D. $\sqrt{2}$

Answer 1

The correct option is D $\sqrt{2}$

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

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

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