Popoviciu's inequality on variances

Popoviciu's Inequality is a mathematical theorem which tells us about the differences between two sets of numbers. It says that if we have a set of numbers which have an average (or mean) of one number, and a different set of numbers which have an average of another number, then the spread (or variance) of the second set of numbers must be at least as much as the spread of the first set of numbers. To understand this, imagine you have two boxes of apples. One box has 10 apples, and their average weight is 5 ounces. The other box has 20 apples, and their average weight is 10 ounces. Popoviciu's Inequality says that the variance (or spread) of the weights for the second box must be at least as much as the spread of the weights for the first box.