The outcome of each of 30 items was observed; 10 items gave an outcome 12-d each, 10 items…

Question

The outcome of each of 30 items was observed; 10 items gave an outcome $\dfrac12-d$ each, 10 items gave outcome $\dfrac12$ each, and the remaining 10 items gave outcome $\dfrac12+d$ each. If the variance of this outcome data is $\dfrac43$ then $|d|$ equals:

Accepted Answer

Mean $= \dfrac12$.

$$\sigma^2 = \frac{1}{30}\left[10\left(\frac12-d\right)^2+10\left(\frac12\right)^2+10\left(\frac12+d\right)^2\right]-\frac14$$

$$\frac43 = \frac{1}{30}\left[30\times\frac14+20d^2\right]-\frac14 = \frac14+\frac23d^2-\frac14$$

$$d^2=2 \implies |d|=\sqrt2$$

Solutions · 1