Basu (1958) and Raj and Khamis (1958) have shown that in sampling with replacement the average over distinct units possesses lower variance than the average over the entire sample, including repetitions. While Basu proves the result by the use of the Rao-Blackwell theorem, Raj and Khamis prove it by making use of the distribution of the number of distinct unitsuin the sample, and the proof is quite involved. Here, an elementary algebraic proof is given.