Is there a word in statistics for "mean divided by absolute difference"?

For two values, let’s say a and b, I calculate a mean of two numbers divided by absolute difference between them. i.e.

((a+b)/2)/|a-b|

This statistic represents the change in the mean per unit difference.

I looked around to see if there is any name in statistics for this statistic. But I could’t find any.
Please let me know if you are aware of the name (possibly a jargon!) in statistics for such a statistic.