If each of given $n$ observations is multiplied by a certain positive number $'k'$, then for new set of observations -
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 $............$.
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 $...........$.
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 $...........$.
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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
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
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
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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
$3$
$4$
$7$
$7$
$15$
$9$
$6$
$6$
$3$
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 | $3$ | $4$ | $7$ | $7$ | $15$ | $9$ | $6$ | $6$ | $3$ |