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 $\sum_{i=1}^{5}(x_i-10)=5$ and $\sum_{i=1}^{5}(x_i-10)^2=5$ then standard deviation of observations $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7$ and $2x_5 + 7$ is equal to-
Mean and standard deviation of 100 observations were found to be 40 and 10 , respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.
The means of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$, then the other two are
The variance of first $50$ even natural numbers is
Find the mean and variance for the data
${x_i}$ | $92$ | $93$ | $97$ | $98$ | $102$ | $104$ | $109$ |
${f_i}$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |