# Expressing a range that excludes the two outermost members of the range

I have a number of calibration standards (solutions that contain binding antibodies in exact quantities). The lowest-concentration standard is 200 ng/mL, the highest is 5000 ng/mL. Between them, there are standards with concentrations of 250, 300, and so forth.

The permitted deviation of concentration for the highest and lowest standards is 25%, while the permitted deviation for the other standards is 20%.

How do I indicate in writing that the range I'm describing in sentence 2 (below) excludes the two "outermost" standards?

The measured concentration of binding antibodies in the calibration standards (concentrations: 200 and 5000 ng/mL) should not deviate by more than 25 % from the nominal concentration.

The measured concentration of binding antibodies in the calibration standards (concentrations: from 200 to 5000 ng/mL) should not deviate by more than 20 % from the nominal concentration.

Should I write "concentrations: above 200 but below 5000 ng/mL"? This looks a bit out of style for technical writing. There must be some elegant way of expressing this.

Could "concentrations: between 200 and 5000 ng/mL" be a suitable choice?

You could write

The measured concentration of binding antibodies in the calibration standards (concentrations: from 250 ng/mL to 5000 ng/mL exclusive) should not deviate by more than 20% from the nominal concentration.

The typical usage for "exclusive" when describing a range just excludes the last number, so I started the range at the first non-excluded concentration. For example, "1 to 5 exclusive" would be "1,2,3,4". Since there are only two numbers you want to exclude, you could also just say:

The measured concentration of binding antibodies in the calibration standards (excluding concentrations 200 ng/mL and 5000 ng/mL) should not deviate by more than 20% from the nominal concentration.

I prefer the second sentence, because it parallels the first sentence a bit better.

...calibration standards (concentrations 200 ng/mL and 5000 ng/mL) should not deviate by more than 25%...
...calibration standards (excluding concentrations 200 ng/mL and 5000 ng/mL) should not deviate by more than 20%...

I don't like the space between the number and the percentage sign so I removed them, but if that's what your style guide says to do it's fine. I also added the "ng/mL" to the 200 calibration so that it would parallel the second sentence.

Most of the relevant search hits I found using "excluding concentrations" are behind pay walls. I will see if I can find some relevant usage and add it.