When each number in a set is multiplied by a value, how does that affect the standard deviation?

When each number in a set is multiplied by a value, the standard deviation of the set is affected directly by that multiplier. The standard deviation measures the amount of variation or dispersion in a set of numbers. When each number is scaled by a constant factor, the spread of the numbers changes proportionally to that factor.

Specifically, if all numbers in the set are multiplied by a certain value, the new standard deviation will be equal to the original standard deviation multiplied by that value. This directly reflects how the spread of the numbers is impacted by the multiplication. Therefore, the relationship between the number of the set and its standard deviation shows that the standard deviation changes by the multiplied value, confirming the correctness of the selected answer. This principle is a key aspect of understanding how transformations affect statistical measures.