When should one of mean, mode, and median be used over the other
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The mean on its own intuitively explains “normal” data, or distributions with a big spike right in the middle that taper off symmetrically on each end.
The median is useful to add to the median if the data is “skewed” (leans in one direction) or has “outliers” (some data points that are way high or low and drag around the mean). A good example is household income, where a few super wealthy households drag up the mean income so that the mean overstates the wealth of the “typical” person, which may be better described by the median.
A mode is most useful for qualitative data like “favorite ice cream flavor”, but could potentially add info to a distribution with an unexpected spike in it. For example, if the mean on a test was a 75 but the mode was an 84… consider the possibility that some kids cheated together.
Of course, this is all an oversimplification. It’s best practice to include mean and median when describing distributions (they will be about the same in normal data). The standard deviation is also important info to include to describe how quickly the data tapers off.
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