- Home
- Standard 11
- Mathematics
13.Statistics
medium
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
A
$1$
B
$\frac{9}{4}$
C
$\frac{4}{9}$
D
$\frac{2}{3}$
(AIEEE-2006)
Solution
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, $\quad V_{A}=V_{B}$
$\Rightarrow \quad \frac{V_{A}}{V_{B}}=1$
Standard 11
Mathematics
Similar Questions
Find the mean and variance for the data
${x_i}$ | $92$ | $93$ | $97$ | $98$ | $102$ | $104$ | $109$ |
${f_i}$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |
hard