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13. statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS13. statistics1 Mark
MCQ
Suppose a population $A $ has $100$ observations $ 101,102, . . .,200 $ and another population $B $ has $100$ observation $151,152, . . .,250$ .If $V_A$ and $V_B$ represent the variances of the two populations , respectively then $V_A / V_B$ is
  • ✓
    $1$
  • B
    $\frac{9}{4}$
  • C
    $\frac{4}{9}$
  • D
    $\frac{2}{3}$
✓

Answer

Correct option: A.
$1$
a
Series $A=101,102 \ldots \ldots 200$

Series $\mathrm{B}=151,152 \ldots \ldots .250$

Here series $\mathrm{B}$ can be obtained if we change the origin of $A$ by $50$ units.

And we know the variance does not change by changing the origin.

So, $\quad V_{A}=V_{B}$

$\Rightarrow \quad \frac{V_{A}}{V_{B}}=1$

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