Nomographic Interpolation of Income Size Distributions - Liebenberg, Maurice (The Review of Economics and Statistics, 1956)
M OST of the statistical procedures used in the manipulation of income size distributions involve interpolation in some form.' The worker is frequently concerned with such problems as the determination of decile points, medians, or, in general, some income points which are meaningful for subsequent analysis or presentation. Such problems reduce, in the practical case, to the task of finding the upper limits of subintervals the frequencies of which are known. In addition to such problems, most adjustments made to distributions involve the modification of the income variate in some manner, as is the case when a given relative distribution is maintained by multiplying all incomes by a constant, or when the relative distribution is changed by modifying incomes differentially. After such shifts the initial classification of units by size of income has changed, and interpolation is required to determine the changed distribution of frequencies in the initial classes. In this type of problem the interpolated income point is known, and it is necessary to determine the frequency in the subinterval of which the known point is the upper limit. This paper presents a practical alternative to the usual graphic or computational methods of interpolation. Nomographic charts are given which incorporate formulas that have been used successfully to interpolate for income points, frequency, and income. In the sections that follow, the usual methods will be examined briefly, the basic formulas underlying the nomograms presented, and the steps in their use outlined for several types of interpolation problems. Need for Alternatives to Usual Methods