and income inequalityThe first step in advancing the proposal for measuring inequality is to remember that there are two series[22] in the distribution: one of incomes (attribute), the other of frequencies. The income series is formed by the set of incomes earned in the various economic activities by wage-earners, employers and self-employed workers. The frequency series is formed by the set of individuals who perform activities in their respective occupations (wage-earners), functions (employers) and provision of services (self-employed).The different movements of the two series over time, from one period to another, are related to changes in income gains in the income series, which distinguish the groups of individuals, and to changes in the occupations, functions and services in the frequency series, which regroup the individuals in the income intervals.The second step is to remember that the income distribution table can be viewed and understood as a count of the frequencies in their respective income ranges and as a position scale in the distribution, referenced by the income levels of each range. These two features of the table are important to show the movements of incomes and frequencies from t-1 to t.The third step is to include the two series in an income inequality measure, in which each can be adapted and delimited separately. Adapted in the sense of converted to a mathematical dimension compatible not only in its numerical expression, but also in the precise characterization of its contents. Delimited in the sense of having its numerical magnitude determined, each different from each other.In order for the income and frequency series to be adapted, therefore, their initial expressions (values and numbers) are converted to comparable magnitudes. This is done because incomes are originally measured in monetary units and frequencies are presented in different numerical quantification.The chosen form of conversion, which should be compatible with the desired comparable magnitudes, is intended to obtain incomes and frequencies in relative values, i.e. participations. So the participations of each average income (yi) are obtained, referring to each income range (ri) in the total income distribution, and the participations of each frequency group in the total sum (N) of the frequencies or relative frequencies (ni).In fact, the conversion does not alter the series of absolute average incomes, representative of the income intervals (or ranges, or classes) nor the frequency series, it only adjusts the dimensions of the series to make them comparable percentagewise. Thus (ri) is the multiplication of two terms(yiY), where yi is the average income of the i interval and Y is the average income of the entire distribution, and (niN) is the relative frequency corresponding to average income yi.The only series, in fact, whose form is altered is that of incomes. However, it continues to indicate its characteristic of ordering or scaling of the relative frequencies around the relative incomes (yiY). Variations in relative incomes take relative frequencies up or down the income ladder, which is an approximation of the position ladder.With the conversion of incomes and frequencies into comparable magnitudes, the following algorithm is obtained:(1) (ri ni)2 = (ri)2 + (ni)2 - 2(ri)(ni)If