Weighted Mean

A weighted mean is used when not every value should contribute equally to the average. Each value is multiplied by a weight that shows its importance, frequency, or size, and then the weighted totals are divided by the total of the weights so the result stays on the same scale as the original values. This works because it is equivalent to counting values more times when they matter more, instead of treating every observation as identical.

Use this formula when combining measurements or scores that do not all count the same, such as test scores with different point values, average prices with different quantities bought, or sensor readings collected for different lengths of time. It is especially useful whenever the data come with frequencies, proportions, credits, or importance levels.

• Using the raw average instead of multiplying each value by its weight first
• Forgetting to divide by the sum of the weights
• Treating percentages, frequencies, and probabilities as if they were all the same without checking their total