Item 4 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?

In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.

How to determine the variance of the transformed sample?

Let x represent the original random sample. Therefore, the variance of x will be equal to 4:

Var(x) = 4

Mathematically, the variance of the transformation is given by;

y = 3x + 10

From the property of variance, we have:

Var(y) = a²Var(x)

Substituting the given parameters into the formula, we have;

Var(y) = 3² × 4

Var(y) = 9 × 4

Var(y) = 36.

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