If each observation of a raw data whose variance is ${\sigma ^2}$, is multiplied by $\lambda$, then the variance of the new set is
${\sigma ^2}$
${\lambda ^2}{\sigma ^2}$
$\lambda + {\sigma ^2}$
${\lambda ^2} + {\sigma ^2}$
Given that $\bar{x}$ is the mean and $\sigma^{2}$ is the variance of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$ Prove that the mean and variance of the observations $a x_{1}, a x_{2}, a x_{3}, \ldots ., a x_{n}$ are $a \bar{x}$ and $a^{2} \sigma^{2},$ respectively, $(a \neq 0)$
The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -
Find the variance and standard deviation for the following data:
${x_i}$ | $4$ | $8$ | $11$ | $17$ | $20$ | $24$ | $32$ |
${f_i}$ | $3$ | $5$ | $9$ | $5$ | $4$ | $3$ | $1$ |
The mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.80.$ Then which one of the following gives possible values of $a$ and $b$ $?$
The mean and variance of $7$ observations are $8$ and $16,$ respectively. If five of the observations are $2,4,10,12,14 .$ Find the remaining two observations.