Several Approaches for Measuring Average Rates of Change for a Second Degree Polynomial

Abstract

Sometimes it is desirable to obtain single summary estimates of rates of change for curved lines. For example, an investor may be interested in what is likely to be his yearly capital gains and may be willing to ignore fluctuations over shorter time intervals, even if they are real. A biologist may w-ish to examine average growth per unit time in an organism whose growth is exactly described by a second degree curve. Further, comparisons of rates of change for tw o populations may be required where one is linear and the other curvilinear. In this paper we shall discuss some statistics that might be employed to characterize rates of change for the second degree curve and examine the ways in which they differ.