Mean of mean and average
No, it sounds like an odd metric. I suspect the parametric distributions often calculable for the median and mean would be rather nasty for the average of the two which would make this unpopular among statisticians.
I suspect you mean &quot;outliers&quot; by extreme values. If you consider the definition of an outlier:

In statistics, an outlier is a data point that differs significantly from other observations.

https://en.wikipedia.org/wiki/Outlier
(I checked a few definitions and most of them are like this).
I think on a discrete scale of 1 to 5, the idea of an outlier sounds odd. As you can see &quot;differs significantly&quot; is open to interpretation and I don't think 1 or 5 differ greatly from 2-4 unless the rest of your user ratings are at 3 only.
In any case, it is probably best to just use the mean. If you lack the variation in the data to seperate out the objects you want using the mean +- std dev or confidence intervals then that's just the data and there's not much you can do about it.