A) \[\frac{2}{3}\]
B) \[\frac{\sqrt{5}}{2}\]
C) 2
D) \[\sqrt{2}\]
Correct Answer: D
Solution :
Since, variance is independent of origin, so we shift the data by \[\frac{1}{2}.\] Now, mean of the given items\[=\frac{-10d+0+10d}{30}=0\] Now, variance \[=\frac{10{{d}^{2}}+10\times {{0}^{2}}+10{{d}^{2}}}{30}-{{(0)}^{2}}=\frac{4}{3}\] \[\Rightarrow \frac{20}{30}{{d}^{2}}=\frac{4}{3}\,\,\,\,\,\,\,\,\,\Rightarrow d=\pm \sqrt{2}\] \[\therefore \]\[|d|=\sqrt{2}\]
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