Q56 / 125 · BITSAT 2012 · Mathematics
If sample A contains 100 observations $101,102, \ldots$ 200 and sample B contains 100 obsections $151,152,$ \ldots 250, then ratio of variance $\mathrm{v}_{\mathrm{A}} / \mathrm{v}_{\mathrm{B}}=$
- Correct answerA1
- B$\frac{9}{4}$
- C$\frac{4}{9}$
- D$\frac{2}{3}$
Solution
$\because \quad \delta_{\mathrm{x}}^{2}=\frac{\Sigma \mathrm{d}^{2} \mathrm{i}}{\mathrm{n}}$
But both $A$ and $B$ have 100 observations, then both the sample $A$ and $B$ have same standard deviation and the same variance.
Hence, $\frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}}=1$
Hence, the correct answer is option: 'A'.