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There are a number of different ways of averaging a dataset, each with a specific definition. For example,

  • mean: Sum of $N$ values divided by $N$
  • median: The $(N+1)/2$ term after $N$ values are sorted
  • mode: The most common value in a dataset

I am looking for a term for the $(\text{min}+\text{max})/2$, the 'middle' of a set of data. Is there a specific term for this definition already?

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The term you are looking for is "mid-range". For reference, see https://en.wikipedia.org/wiki/Mid-range