Is there a word to describe either under or overweight? I simply want a single word that would mean "this is the amount that is - or + the normal weight range".
I am thinking of either 'deviation' or 'discrepancy', any of them is good for this usage?
The word will be followed by a number with a sign (+,-).
So, deviation is a reasonably correct use of a statistical term. It refers to the difference between an observed value and some reference value - usually the reference value is the mean, but not always. All we have here is a reference value that's actually a range, but it isn't much of a stretch.
On the other hand, depending on the audience you may wish to avoid that term for this particular value. If it's being used by the public, the lack of statistical education would likely mean some would take it as being insulting, that being overweight or underweight is "deviant" in a moralistic sense.
A brief bit of digging suggests that any other term would be a much more novel coining, however. If the audience is statisticians or clinicians, you can definitely use deviation, but you should take clear to carefully define it before use (if this is for a document) or in unavoidable bits of user interface (if this is for software).
I don't agree with "deviation" because, in mathematics, deviation is a measure of difference between a specific value and some other value. You are talking about a value being outside of a range. In statistics, deviation is often used to define a range - for example, if you take a single value such as a mean average, you can define a range by calculating several standard deviations above and below that value. As you already have a range defined, this term is not only gramatically inappropriate, but to anyone with a knowledge of statistics or mathematics it is just confusing.
"Discrepancy" is not appropriate either I'm afraid - it also refers to the difference between two specific numbers, but also implies a mistake.
I'm not sure that you will find a suitable single word for this context. If you are trying to avoid the terms "overweight" and "underweight", you would be better referring to your range by name (for example, BMI, if that is the range you are using) and simply say that someone is "above" or "below" that range. If you must have a single term, perhaps "out-of-range"?
As a heading in a table, deviation works well, provided there is context to support it:
This table shows the mass of each loaf of bread, and the deviation from the weight claimed on the label
shape mass deviation round 450g +50 tin 780g -20
In general writing, you should rephrase:
The first loaf was fifty grams heavier than the weight claimed on the packaging, but the second was 20 grams lighter.
You can say "The first loaf deviated by +50g" but this is not a common way to express this.
This gets socially complex if you start talking about people. Weight is something that people see as being personal to them. The same language of "deviation" is possible, but be aware that some will find this insulting.
I would use different from in a sentence, or Difference as a table header. Different/Difference indicates that it's an observation, not a judgment. Not making any mention of over/under reinforces that. For example:
His weight is 10 pounds different from the ideal weight.
(I acknowledge that many will assume it's higher than the ideal weight, but that's a cultural bias)
I ended up using 'Status', it's the best option I could come up with. It will also not be "insulting" to people, IMO.
