In math absolute value means the distance of a number from zero, regardless of direction. The absolute value of 3 is 3, the absolute value of negative 3 is 3. The absolute value of something is always non-negative.
Some folks use the term absolute value in a way that adds ambiguity. Last week the US Environmental Protection Agency said that servers and datacenters accounted for 1.5% of all US power consumption in 2006. By itself that’s a stunning statistic. But then the EPA said that the absolute value is twice what it was five years ago. Maybe the EPA was referring to actual power consumption, not the percentage, but that’s not what they wrote.
Absolute value seems to be a difficult concept even for academics.
The University of Massachusetts gets it wrong in their glossary, saying the absolute value of x-m is the same as m-x, which it’s not when x is greater than m. What are they teaching their math students there?
The US Department of Transportation gets is wrong, too: it says the absolute value of -(10x + 4) is the same as (10x + 4) but it’s not when x is less than -2 1/2. I hope they do a better job of transporting things.
Princeton University says it’s a numerical value regardless of its sign. That’s not exactly right either: what if the numerical value is less than zero? I’m sure Einstein didn’t come up with that definition.
One thing is clear: government and higher education do not absolutely value – or properly use – common math terms.