The variance of 10 observations is 16 and their mean is 12 .if each observation is multiplied by 4, what are the new mean and the new variance?
ANS : MEAN- 48
VARIANCE-64

Step-by-step 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

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