The value of Elderton's k - criterion can be bounded for a given pdf. This paper presents these bounds for the most widely used distribution functions for income and computes the value of K for household incomes as reported in the Consumer Population Survey. The variance for theK are also estimated using the bootstrap, jackknife and delta methods. We find that the K can be used to narrow the field of potential pdfs for income and that all three methods for estimating the variance coincide in flagging low precision in the estimated K.