If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox.

Examples

Basic example

Given two school classes{{tspmdash}}tsp}}one}} with 20 students, one with 30 students{{tspmdash}}tsp}}and}} test grades in each class as follows:

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