If each of given $n$ observations is multiplied by a certain positive number $'k'$, then for new set of observations -

  • A

    variance will be unchanged.

  • B

    new variance will be $k$ times old variance

  • C

    standard deviation will be unchanged.

  • D

    new standard deviation will be $k$ times old standard deviation

Similar Questions

If the mean and variance of the frequency distribution

$x_i$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$
$f_i$ $4$ $4$ $\alpha$ $15$ $8$ $\beta$ $4$ $5$

are $9$ and $15.08$ respectively, then the value of $\alpha^2+\beta^2-\alpha \beta$ is $............$.

  • [JEE MAIN 2023]

Let the mean and variance of $8$ numbers $x , y , 10$, $12,6,12,4,8$, be $9$ and $9.25$ respectively. If $x > y$, then $3 x-2 y$ is equal to $...........$.

  • [JEE MAIN 2023]

If the mean deviation about median for the number $3,5,7,2\,k , 12,16,21,24$ arranged in the ascending order, is $6$ then the median is

  • [JEE MAIN 2022]

Let the mean and variance of $12$ observations be $\frac{9}{2}$ and $4$ respectively. Later on, it was observed that two observations were considered as $9$ and $10$ instead of $7$ and $14$ respectively. If the correct variance is $\frac{m}{n}$, where $m$ and $n$ are co-prime, then $m + n$ is equal to

  • [JEE MAIN 2023]

Find the mean, variance and standard deviation using short-cut method

Height in cms $70-75$ $75-80$ $80-85$ $85-90$ $90-95$ $95-100$ $100-105$ $105-110$ $110-115$
No. of children $3$ $4$ $7$ $7$ $15$ $9$ $6$ $6$ $3$