Does Variance depend on change of scale and origin? I know that SD depends on change of scale and not on change of origin.  
But what about Variance? And why?
 A: Here is a numerical example with fake data: 100 observations $X_i$ simulated
from a normal distribution with population mean 50 and population SD 3. Now it is easy to give a numerical illustration of the formulas in the comments.
The sample mean is $\bar X = 49.82$; the sample variance is $S_X^2 = 8.05$;
and the standard deviation is $S_X = 2.84.$ (BTW: As is typical with 100 such observations,
$\bar X$ is pretty close to the population mean, and $S_X$ has a somewhat
larger percentage error. Population means are easier to estimate with
accuracy than are population standard deviations.)
Now I add 10 to all $n = 100$ observations: $Y_i = X_i + 10.$ Then
the sample mean is $\bar Y = 59.82$; the sample variance is $S_Y^2 = 8.05$;
and the standard deviation is $S_Y = 2.84.$
Finally, I multiply each of the 100 original 100 observations by 10:
$W_i = 10X_i.$ The results are now as follows: the sample mean is $\bar W = 498.2,$ sample variance is $S_W^2 = 805$; and the
standard deviation is $S_Y = 28.4.$
Note: All numbers have been rounded to a reasonable number of significant
digits for readability.
