How does adding a value to each number in a set affect variance?

When a constant value is added to each number in a data set, the overall variability of the data remains unchanged. Variance is a measure of how spread out the numbers in a data set are from their mean. When you add a constant to each data point, the mean of the data set shifts by that same constant value. However, the differences between each data point and the mean, which are used to calculate variance, do not change.

To illustrate this, consider a simple example. If you have a data set {2, 4, 6} and its mean is 4, the variance calculated would reflect how far these numbers are from 4. Now, if you add 3 to each of these numbers, you get a new set {5, 7, 9}, which has a mean of 7. Even though both the mean and each data point have changed, the spread between the numbers relative to the mean remains the same. Thus, the variance calculated from both sets will be identical, leading to the conclusion that adding a constant to each value does not affect the variance.