Understanding Experimental Data Dispersion

Abstract

Few, if any, scientific conclusions rest on single experimental measurements, hence some method is needed to express the dispersion of experimental results about some measure of central tendency, typically, the arithmetic mean. The range is one possibility. If the arithmetic mean of a large set of experimental data is 123 with a range of 110–135, we would assume, and usually rightly, that the scatter or experimental error of this set is less than that of a set with $\bar{x} = 123$ and a range of 100–150.