Question

Each value in a sample has been transformed by multiplying by 3 and then adding 10. If the original sample had a variance of 4, what is the variance of the transformed sample?

a. 36
b. 14
c. 12
d. 10

Answer 1

The variance of the transformed sample, after each value is multiplied by 3 and then increased by 10, is 36.

Step-by-step explanation:

The question pertains to the effect of a linear transformation on the variance of a data set. When each value in a sample is transformed by multiplying by 3 and adding 10, the new variance can be calculated by squaring the multiplication factor and then multiplying it by the original variance. Therefore, the new variance is (3^2) × 4 = 36.