I'm not sure I fully understand your question, you're asking for avg to serve as a dimension, and count as a measure.
Because there can be only one average, unless you want to split it some how, it doesn't make much sense.
Anyway, I think what you need is a scatter plot, See attached image, from the 'Help-desk management' app:
X - Avg Case duration
Y - Count of cases
I hope it makes sense.