Rel between Range and Mean/Median in Even Spaced Set

In an evenly spaced set, the
1) mean = median
2) mean = (first + last)/2

The range in a set is the highest value - the lowest value.
Or in an evenly spaced set: last - first = range

In general, is there any relationships between the range and the mean in the evenly spaced set? I am trying to find connections so I can strategize how to attack a range/mean problem.

I guess that if I'm given the range and the the highest value, I can then in turn find the lowest value.
Using these highest and lowest values, I can find the mean (lowest + highest)/2.

Thanks,
Francis