If each of given $n$ observations is multiplied by a certain positive number $k$,then for the new set of observations -
- Avariance will be unchanged.
- Bnew variance will be $k$ times old variance.
- Cstandard deviation will be unchanged.
- Dnew standard deviation will be $k$ times old standard deviation.
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Similar Questions
Consider the following frequency distribution: $C$.$I$. $75$-$175$ $175$-$275$ $275$-$375$ $375$-$475$ $475$-$575$ $575$-$675$ $675$-$775$ $f_i$ $3$ $2$ $1$ $0$ $1$ $2$ $3$
If the variance of this distribution is $60000$,then the coefficient of variation of the distribution is:
| $C$.$I$. | $75$-$175$ | $175$-$275$ | $275$-$375$ | $375$-$475$ | $475$-$575$ | $575$-$675$ | $675$-$775$ |
| $f_i$ | $3$ | $2$ | $1$ | $0$ | $1$ | $2$ | $3$ |
Variance of first $n$ natural numbers is $\qquad$ .
The variance of the following frequency distribution is:
Class Interval $0$-$4$ $4$-$8$ $8$-$12$ $12$-$16$ $16$-$20$ Frequency $2$ $4$ $6$ $3$ $1$
| Class Interval | $0$-$4$ | $4$-$8$ | $8$-$12$ | $12$-$16$ | $16$-$20$ |
| Frequency | $2$ | $4$ | $6$ | $3$ | $1$ |
If the variance of four numbers $w, x, y,$ and $z$ is $9$,then the variance of $5w, 5x, 5y,$ and $5z$ is:
The mean and variance of six observations are $8$ and $16$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations is:
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