Calculating average with minimum and maximum

Question

Maybe it's a simple question but I have not any idea for that at the moment!

How we can calculate average value for N samples with having only the minimum and maximum values?

Answer 1

You can't. Compare with $0,1,8$ and $0,7,8$.

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In fact, the average can be anywhere in

$$\left[\frac{(n-1)\min+\max}n,\frac{\min+(n-1)\max}n\right],$$

and if the distribution is skewed, the average of the minimum and maximum will be biased.

Answer 2

In general, you can't. If you have two samples of numbers, let's say $$\{0,2,3,1,1,1,8\}\quad \text{and} \quad \{0,7,7,6,4,8,8\}$$ the average of these samples will be different, but they have the same maximum and minimum values. If you're only given the maximum and minimum, you could make a guess that the average is $\frac{\text{max}+\text{min}}{2}$, but it's probably not a good guess.