On the Range of a Series of Observations

Abstract

Allow me to add two remarks to the address by Mr. L. von Bortkiewicz on “Range and Standard Deviation” that was published in these Proceedings.(¹) I believe these remarks will usefully supplement the interesting points made by the speaker. One remark includes a simple and general derivation, not restricted to the assumption of a Gaussian law, of the formula for the expected value of the range. In the second, I provide an asymptotic expression for this expectation, also for a larger class of distributions. For the case of the Gaussian law this expression reduces to a final formula that is very simple, useful in practice, and even instructs us how to find the desired value, without any calculation, in the standard tables of the Gaussian integral.