What happens to variance when each number in a set is divided by a value?

When each number in a set is divided by a value, the correct outcome for variance involves dividing by the square of that value. Variance is a measure of the spread of numbers in a data set, and it is calculated based on the squared differences from the mean.

When you scale the numbers in the data set, this transformation affects how spread out the numbers are concerning the mean. If each number is divided by a value, the effect on variance stems from how variance is inherently calculated using squared differences. Thus, if you divide each value by a constant ( k ), the variance of the transformed data set will be ( \frac{\sigma^2}{k^2} ), where ( \sigma^2 ) is the original variance. This is because the distance to the mean (which is involved in calculating variance) gets scaled by the same factor ( k ).

As a result, the variance is not simply divided by the value itself but rather by the square of that value, reflecting the squared nature of the variance calculation. This understanding is crucial when working with statistics and transformations of data sets.