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The literature on population ageing includes two measures of the median age. One is the conventional median age and the other is the prospective median age. The prospective median age adjusts the median age for changes in remaining life expectancy. In this paper, we study the properties of these two measures. Surprisingly, annual changes in these two measures in life table populations are of roughly equal magnitude, but of opposite sign. We show that demographic theory predicts that this would be the case. Because the changes are of opposite sign, the choice of which median age to use in analyses is crucial.