Weighted average versus simple average
When to weight your numbers and when a plain mean will do, with grade, finance and survey examples that show how weighting changes the answer.
The core difference
A simple average adds up your values and divides by how many there are, giving every entry an identical say. A weighted average instead assigns each value a weight, multiplies value by weight, sums those products, and divides by the total weight. The effect is that heavier items pull the result toward themselves. When all the weights match, the two methods return exactly the same number, so weighting only matters when some values deserve more influence than others.
Grades and grade point averages
School is the most familiar place to meet weighted averages. A syllabus might set homework at 20 percent, a midterm at 30 percent and a final at 50 percent, so the same score on the final shifts your grade far more than on homework. A grade point average works the same way, using credit hours as weights so a four-credit course counts more than a one-credit seminar. Enter each score as a value and its weight or credits as the weight to reproduce your transcript.
Money and measurement
Finance leans on weighted averages constantly. A portfolio return is the return of each holding weighted by how much money sits in it, and a weighted average cost of capital blends the cost of debt and equity by their share of financing. Laboratories and surveys weight readings by sample size or reliability so a measurement from a thousand people outweighs one from ten. In each case the weight represents importance, size or confidence rather than a simple count.
Choosing the right weights
The quality of a weighted average depends entirely on the weights you pick, so decide what the weight should represent before you start. It might be a percentage, a number of credits, a dollar amount or a sample count, but it must be consistent across every row. You do not need the weights to sum to one hundred, since the calculator divides by their total, but they should be on the same scale. A single mismatched weight quietly distorts the whole result.