Q57 / 150 · JEE Main 2006 · Mathematics

Suppose a population $A$ has 100 observations $101,102, \ldots, 200$, and another population $B$ has 100 observations $151,152, \ldots, 250$. If $V_A$ and $V_B$ represent the variances of the two populations, respectively, then $\frac{V_A}{V_B}$ is

  • Correct answer
    A
    1
  • B
    9/4
  • C
    4/9
  • D
    2/3

Solution

$\sigma_x^2=\frac{\sum d_1^2}{n}$. (Here deviations are taken from the mean) Since $A$ and $B$ both has 100 consecutive integers, therefore both have same standard deviation and hence the variance. $\therefore \frac{V_A}{V_B}=1\left(\right.$ As $\sum d_i^2$ is same in both the cases).

Hence, the correct answer is option: 'A'.

Relevant Questions