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

  • [AIEEE 2006]
  • A

    $1$

  • B

    $\frac{9}{4}$

  • C

    $\frac{4}{9}$

  • D

    $\frac{2}{3}$

Similar Questions

The diameters of circles (in mm) drawn in a design are given below:

Diameters $33-36$ $37-40$ $41-44$ $45-48$ $49-52$
No. of circles $15$ $17$ $21$ $22$ $25$

Calculate the standard deviation and mean diameter of the circles.

[ Hint : First make the data continuous by making the classes as $32.5-36.5,36.5-40.5,$ $40.5-44.5,44.5-48.5,48.5-52.5 $ and then proceed.]

Let $x _1, x _2, \ldots \ldots x _{10}$ be ten observations such that $\sum_{i=1}^{10}\left(x_i-2\right)=30, \sum_{i=1}^{10}\left(x_i-\beta\right)^2=98, \beta>2$ and their variance is $\frac{4}{5}$. If $\mu$ and $\sigma^2$ are respectively the mean and the variance of $2\left( x _1-1\right)+4 \beta, 2\left( x _2-1\right)+$ $4 \beta, \ldots . ., 2\left(x_{10}-1\right)+4 \beta$, then $\frac{\beta \mu}{\sigma^2}$ is equal to :

  • [JEE MAIN 2025]

The average marks of $10$ students in a class was $60$ with a standard deviation $4$, while the average marks of other ten students was $40$ with a standard deviation $6$. If all the $20$ students are taken together, their standard deviation will be

The mean and variance of seven observations are $8$ and $16$, respectively. If $5$ of the observations are $2, 4, 10, 12, 14,$ then the product of the remaining two observations is

  • [JEE MAIN 2019]

The data is obtained in tabular form as follows.

${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$