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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.

kjetil b halvorsen
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    It's unusual because $|a-b|$ often will be small or zero, making it an unstable and sometimes undefined statistic. People generally prefer to use its reciprocal, the RPD. (It's exceedingly rare to see anyone conceive of a mean depending on a difference.) See https://stats.stackexchange.com/a/201864/919 for a discussion. – whuber Jul 22 '20 at 20:51

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