Assign + or - to the result of a formula based on the number with highest absolute value?

Hello, I'm a research scientist analyzing some data for a behavioral task my colleagues and I invented. I've developed an informative metric from the data that I understand and can explain conceptually, and can certainly calculate by hand, but am having difficulty figuring out how to get Excel to do it as a formula. Here's a summary of the problem via example:

Start with a series of numbers; some will be positive and some negative (for example: 50, -100, 25)
Determine the absolute range within the series (MAX - MIN); in this case [50] - [-100] = 150
I'm not sure if it matters, but the particular metric I'm developing then divides that number by 2 (150 / 2 = 75)
So the final formula = (MAX(series) - MIN (series))/2

All the steps above work just fine and do what I need; however, the number constituting the final result of that formula must be assigned + or - based on the member of the series with the highest absolute value. In the example above, the result of the formula = 75, which is indeed the absolute range divided by 2, but the final number needs to be -75 because the member of the series with the highest absolute value = -100.

Obviously hand calculation and visually scanning the data are fine for brainstorming/development, but not a reliable approach for high-throughput data processing, so any insight or advice would be most appreciated!

Wow, thank you so much! Clearly the Force is very strong with both of you. I wound up going with tigeravatar's "Alternate solution" (the "Shorter version" didn't seem to work out, not sure why) because it was copy-and-paste. However, thank you mrice for the User Defined Function; I don't have much experience with that approach, so this is an excellent opportunity to get my feet wet and improve my repertoire of Excel skills.

This was the first time I've ever participated in any online forum, and it's nice to know that there are good people out there in the world who are willing to help a perfect stranger--I'll surely pay it forward. Thanks again...