What is a characteristic of the weighted mean?

The weighted mean is a statistical measure that takes into account the varying degrees of importance or weight assigned to different observations in a data set. This characteristic allows the weighted mean to provide a more nuanced average when certain data points are deemed more significant than others. For example, in a scenario where different tests contribute a varying percentage to a student's final grade, the weighted mean would give more importance to tests with a larger contribution.

In contrast, treating all observations equally, as indicated in one of the choices, refers to the regular mean, where every data point is given the same weight. The mention of nominal data reflects a misunderstanding, as the weighted mean is applicable to interval or ratio data, not just nominal. Lastly, while the weighted mean can be calculated from data that may be skewed, it does not preclude its use in these circumstances; thus, skewness of distribution is not a limiting factor for its application.