Some of my pupils came up with a new average, Dale's New Average (DNA) which is the lowest value + range/2. I feel that this is probably not new and ought to have a proper statistical name but don't know what it is.
Does anyone know?
Sounds new to me, and I've been in this field for about 12-13 years.
However, anything that involves the range of the data set in its calculation should be viewed with caution, since the range is extremely sensitive to the idiosyncracies of the sample data set, and is therefore very unreliable.
You may want to run a small simulation to see how it compares to the mean and median in terms of bias, consistency, and relative efficiency.