If each observation of a raw data whose variance is ${\sigma ^2}$, is multiplied by $\lambda$, then the variance of the new set is

  • A

    ${\sigma ^2}$

  • B

    ${\lambda ^2}{\sigma ^2}$

  • C

    $\lambda + {\sigma ^2}$

  • D

    ${\lambda ^2} + {\sigma ^2}$

Similar Questions

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 $b$ $?$ 

  • [AIEEE 2008]

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.