If you multiply each value in a set by 5, how is the variance affected?

When you multiply each value in a set by a constant, the variance of that set is affected by the square of that constant. Variance measures how much the values in a dataset differ from the mean, and it is sensitive to scaling transformations.

In this case, if you multiply each value by 5, you are applying a linear transformation to the dataset. The formula for the new variance after scaling is given by:

New Variance = (k²) × Original Variance

where k is the constant you are multiplying by. Here, since k is 5, the new variance becomes:

New Variance = 5² × Original Variance = 25 × Original Variance.

This demonstrates that the variance multiplies by 5 squared, leading us to the conclusion that the correct answer reflects this principle of variance under scaling transformations.