If you were to multiply a set's variance of 2 by 5, what would the result be?

To understand the effect of multiplying a set's variance by a constant, it's important to recall how variance behaves under scaling. The variance represents how much the values of a set diverge from the mean, and when you multiply each data point in the set by a constant value, the variance is scaled by the square of that constant.

In this case, you start with a variance of 2. If you multiply this variance by 5, you are effectively scaling your data points. However, the variance gets scaled by the square of that multiplying factor. So, you would compute the new variance as follows:

New Variance = Original Variance × (Scaling Factor)²

New Variance = 2 × 5²

New Variance = 2 × 25

New Variance = 50

Thus, by multiplying the variance of 2 by 5 (the constant) squared, you obtain a result of 50. This demonstrates the fundamental property of variance when scaling data: it is directly affected by the square of the constant multiplicative factor. Therefore, the correct answer is 50.