The variance of the ungrouped data $2, 12, 3, 11, 5, 10, 6, 7$ is

In an experiment with $15$ observations on $x$,we have $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

$y_i$	$10$	$18$	$24$	$36$	$42$	$50$	$66$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

Consider $10$ observations $x_1, x_2, \ldots, x_{10}$ such that $\sum_{i=1}^{10}(x_i-\alpha)=2$ and $\sum_{i=1}^{10}(x_i-\beta)^2=40$,where $\alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. The value of $\frac{\beta}{\alpha}$ is equal to :

From the prices of shares $X$ and $Y$ below,find out which is more stable in value:

$X$	$35$	$54$	$52$	$53$	$56$	$58$	$52$	$50$	$51$	$49$
$Y$	$108$	$107$	$105$	$105$	$106$	$107$	$104$	$103$	$104$	$101$

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