If each observation of a raw data whose variance is ${\sigma ^2}$, is multiplied by $\lambda$, then the variance of the new set is
${\sigma ^2}$
${\lambda ^2}{\sigma ^2}$
$\lambda + {\sigma ^2}$
${\lambda ^2} + {\sigma ^2}$
The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. The co-efficient of variation is.....$\%$
The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -
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 :
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.
The data is obtained in tabular form as follows.
${x_i}$ | $60$ | $61$ | $62$ | $63$ | $64$ | $65$ | $66$ | $67$ | $68$ |
${f_i}$ | $2$ | $1$ | $12$ | $29$ | $25$ | $12$ | $10$ | $4$ | $5$ |