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 of the data : $7, 8, 9, 7, 8, 7, \mathop \lambda \limits^. , 8$ is $8$, then the variance of this data is
If the mean of the data : $7, 8, 9, 7, 8, 7, \mathop \lambda \limits^. , 8$ is $8$, then the variance of this data is
- [JEE MAIN 2018]
Find the mean and variance for the first $10$ multiples of $3$
Find the mean and variance for the first $10$ multiples of $3$
The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$
Height
Weight
Mean
$162.6\,cm$
$52.36\,kg$
Variance
$127.69\,c{m^2}$
$23.1361\,k{g^2}$
Can we say that the weights show greater variation than the heights?
The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$
| Height | Weight | |
| Mean | $162.6\,cm$ | $52.36\,kg$ |
| Variance | $127.69\,c{m^2}$ | $23.1361\,k{g^2}$ |
Can we say that the weights show greater variation than the heights?
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 :
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]
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]