Weighted Averages

A plain average treats every number the same. A weighted average doesn't, because the groups behind the numbers aren't the same size or don't count the same amount. If one class has 12 students averaging 90 and another has 18 students averaging 70, the second class pulls harder on the combined average simply because it has more students. Averaging 90 and 70 to get 80 ignores that imbalance completely.

Think of a seesaw. Each value sits at a distance from the center equal to its weight, and the balance point is the weighted average — heavier weights or larger groups pull the balance point toward themselves. The fix is always the same move: multiply each value by its weight, add those products, then divide by the total weight. For the two classes, that's (12 x 90 + 18 x 70) / 30 = (1080 + 1260) / 30 = 78, not 80. The same logic builds a course grade: homework worth 20 percent at 95, tests worth 50 percent at 82, and a final worth 30 percent at 78 give 0.20(95) + 0.50(82) + 0.30(78) = 19 + 41 + 23.4 = 83.4.

This sits right next to center-of-data questions like mean and median, but it's really about unequal groups, which is also the idea behind two-way tables where rows or columns hold different totals. Once a question mentions percents, portions, or different group sizes feeding into one average, it's a weighted average problem, not a simple one.