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In usual statistical analyses, because of diversities of proper parameters of pulsars, some interesting features might be smeared. In order to remove these diversities, we use the mean values for all quantities of pulsars, instead of values of individual pulsar, to do statistical analyses. logP/P3 - log τ and logL - logτ have been plotted, here τ P/2P and L denote the characteristic time scale and the radio luminosity of pulsars respectively. The most striking feature is that after its initial dropping to a dip at about τ∼106 yrs, the radio luminosity of pulsar appears to grow up evidently and then redrop again. This feature is difficult to be understood in usual models. However, two tentative interpretations have been given in this paper.