For $(2n+1)$ observations ${x_1},\, - {x_1}$, ${x_2},\, - {x_2},\,.....{x_n},\, - {x_n}$ and $0$ where $x$’s are all distinct. Let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Then which of the following is always true

  • A

    $S.D. < M.D.$

  • B

    $S.D. > M.D.$

  • C

    $S.D. = M.D.$

  • D

    Nothing can be said in general about the relationship of $S.D.$ and $M.D.$

Similar Questions

The variance of $\alpha$, $\beta$ and $\gamma$ is $9$, then variance of $5$$\alpha$, $5$$\beta$ and $5$$\gamma$ is

The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking it was found that an observation was read as $10$ in place of $12$ . If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15\left(\mu+\mu^2+\sigma^2\right)$ is equal to$...................$

  • [JEE MAIN 2024]

The $S.D.$ of $5$ scores $1, 2, 3, 4, 5$ is

The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2.$ then their new variance is equal to :

  • [JEE MAIN 2023]

Calculate the mean, variance and standard deviation for the following distribution:

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$
$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$