In the architectural and sanitary trades with the advent of ISO certifications it has become necessary switch from old trade terminology such as #4 finish or Mirror finish to measurable surface finishes.
The answer is to quantify these finishes as measurements of surface roughness in micro-inches. Sounds simple enough, what is the depth of the scratches on the surface? More important is what confidence level do we have that the sample taken represents the true surface condition?
This is where the science of statistics comes into play. Here we run into terms like arithmetic mean average, root mean square average, and about four other terms which escape me for now given that it was over 40 years since my last statistics class.
There are little gadgets that drag a point across about one inch of a surface and measure the high and low points in that sample, store them then spit out one of the statistically approved figures for surface roughness of the surface measured. Each means of averaging the high and low points have varying levels of confidence in the accuracy of the measurements. For instance the arithmetic average is accurate to about 94% of the time. The root mean square average is accurate about 97% of the time and so on until 99% confidence is achieved by massaging the numbers obtained from the same sample.
The industries mentioned have decided that an arithmetic average would be sufficiently accurate for their ISO requirements. Therefore the Surface Roughness....R is averaged Arithmetically...A in micro inches giving an number like RA 26 to properly define a surface finish previously known as #4 Brushed Finish, for no other reason than it is measurable and unarguable.
Even mirror finishes can have some undualtion in the surface so it is not impossible to have a mirror with a surface roughness of RA 2 or even RA 3 when the high and low spots in the sample are averaged out
George Tichbourne