What is the actual use of the median and mode in statistics compared to the average (mean)?
In: Mathematics
Median is a good simple way to remove outliers from a data set. For example I have a system that measures a distance. As with all real world systems it has a certain level of noise in the output, averaging the output is a good way to reduce this noise. Most of the time the distance is about correct, you could take the mean and get a very accurate result. But every now and then something goes wrong, it picks up a reflection or some other issue and the result will be completely wrong. E.g. it would measure 10 meters rather than 60.
If I took the mean and this was to happen then my result would be significantly wrong. But such large errors are rare, if instead I use the median these rare outliers are ignored and don’t impact the results.
As others have indicated median is often used when looking at wealth related things like income, it avoids a small number of very wealthy people skewing the results. Any time when you have a small number of significantly different outliers median will often give a better indication of the typical value than mean.
Mode is less commonly used. I can’t think of a time I’ve seen it used in the real world.
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