The mean of the numbers $a, b, 8, 5$ and $10$ is $6$ and the variance is $6.80$. Then the possible values of $a$ and $b$ are:

In a data set with $15$ observations $x_1, x_2, x_3, \ldots, x_{15}$,we are given $\sum_{i=1}^{15} x_i^2 = 3600$ and $\sum_{i=1}^{15} x_i = 175$. If the value of one observation $20$ was found to be incorrect and was replaced by its correct value $40$,then the corrected variance of the data is:

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

In a series of $2n$ observations,half of them are equal to $a$ and the remaining half are equal to $-a$. If the standard deviation of the observations is $2$,then $|a|$ equals:

Let $v_1$ be the variance of $\{13, 16, 19, \dots, 103\}$ and $v_2$ be the variance of $\{20, 26, 32, \dots, 200\}$. Then the ratio $v_1 : v_2$ is:

If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$,then the variance of the data is: