# Calculation of mean value of normal distribution if we only know the maximum and minumum value

If I have only maximum and minimum values, can I calculate mean value of normal distribution?

-
Are you asking if it is possible to determine the average of a sample $x_1,\ldots,x_n$ knowing only $\max_i x_i$ and $\min_i x_i$? – Stefan Hansen Mar 6 '13 at 16:30

## 1 Answer

The distribution itself doesn't have a max and min. Presumably you have a sample from the distribution. The best you can do is take the mean of the max and min. But this will be sensitive to variation in the max and min of your sample, which is much worse than (say) the median of your sample. You can prove that the mean of your sample is an unbiased estimator of the mean of the distribution with less variance than the distribution itself.

-