LetT1andT2be two odd location statistics, such as the sample mean and the sample median. LetS1andS2be two even location-free statistics, such as the sample variance and the sample range. When sampling from a symmetric distribution, it is proved that the conditional expectation of either odd location statistic, given the even location-free statistics, is equal to θ, the midpoint of the distribution. This implies that if the random weightsW1andW2are functions of even location-free statistics so thatW1+W2= 1, thenW1T1+W2T2is an unbiased estimator of θ.