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

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

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If for a distribution $\Sigma(x-5)=3, \Sigma(x-5)^{2}=43$ and the total number of item is $18,$ find the mean and standard deviation.

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${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$