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

Answer: (D)

$\sqrt{2}$

Answer 2

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