What is the actual use of the median and mode in statistics compared to the average (mean)?
In: Mathematics
They each tell you different things about the data set, so the “actual use” would be dependent on what meaning you want to extract from the data set.
Let’s say you’re being graded on something. You do it four times perfectly, 10/10, but you are sick on day, or just have a run of bad luck, and mess it up, 1/10.
You’re “mean” rating would be 8.2. But does that accurately reflect your abilities? Does a single fluke really mean you are 20% less capable than all those other times?
Both the median and the mode would report a value of 10.
The thing to consider and remember is that they are summarizing some aspect of the data, necessarily focusing on some property at the expense of others. With the mean, you sacrifice any information about the distribution of data and are influence by extreme outliers (such as that 1/10 fluke above).
With the mode, you are explicitly being told *something* about the distribution of the data (namely the most common element in the set), but you don’t really know how it compares to the remaining elements of the set.
And, finally, with the median you are learning what the “middle” of the data set looks like while losing information about any extreme outliers.
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