Let the observations $\mathrm{x}_{\mathrm{i}}(1 \leq \mathrm{i} \leq 10)$ satisfy the equations, $\sum\limits_{i=1}^{10}\left(x_{i}-5\right)=10$ and $\sum\limits_{i=1}^{10}\left(x_{i}-5\right)^{2}=40$ If $\mu$ and $\lambda$ are the mean and the variance of the observations, $\mathrm{x}_{1}-3, \mathrm{x}_{2}-3, \ldots ., \mathrm{x}_{10}-3,$ then the ordered pair $(\mu, \lambda)$ is equal to :
$(6, 6)$
$(3, 6)$
$(6, 3)$
$(3, 3)$
If $\sum \limits_{i=1}^{n}\left(x_{i}-a\right)=n$ and $\sum \limits_{i=1}^{n}\left(x_{i}-a\right)^{2}=n a,(n, a>1)$ then the standard deviation of $n$ observations $x _{1}, x _{2}, \ldots, x _{ n }$ is
If the mean and variance of the frequency distribution
$x_i$ | $2$ | $4$ | $6$ | $8$ | $10$ | $12$ | $14$ | $16$ |
$f_i$ | $4$ | $4$ | $\alpha$ | $15$ | $8$ | $\beta$ | $4$ | $5$ |
are $9$ and $15.08$ respectively, then the value of $\alpha^2+\beta^2-\alpha \beta$ is $............$.
If the mean deviation about the mean of the numbers $1,2,3, \ldots ., n$, where $n$ is odd, is $\frac{5(n+1)}{n}$, then $n$ is equal to
In a series of $2n$ observations half of them equals $a$ and remaining half equals $-a$. If the standard deviation of observations is $2$ then $\left| a \right|$ equals
The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4$ and $4;$ then the absolute value of the difference of the other two observations, is