Explanation:
Finding New mean,
If the mean of 10 observations is given as 12,
The sum of the 10 observations, 12×10 = 120.
If each observation is multiplied by 4.
By the associative property, the new sum would be equal to twice the previous sum.
Therefore the new total is 120×4 = 480.
New mean is 480 ÷ 10= 48, twice the previous mean.
New mean = 48.
Finding New Variance,
Variance refers to the average of the sum of squares of differences from the mean.
Every value of the observations is multiplied by 4
where the power is raised of 2, i.e 16
New variance= 16 x 16
= 256