We have analyzed the observed image separations of the gravitationally lensed images of QSOs for a possible correlation with the source redshift .
Contrary to the previously noted anti-correlation based on a smaller data set , no correlation is found for the currently available data .
We have calculated the average image separations of the lensed QSOs as a function of source redshifts , for isothermal spheres with cores in a flat universe , taking into account the amplification bias caused by lensing .
The shape of the distribution of average image separation as a function of redshift is very robust and is insensitive to most model parameters .
Observations are found to be roughly consistent with the theoretical results for models which assume the lens distribution to be ( i ) Schechter luminosity function which , however , can not produce images with large separation and ( ii ) the mass condensations in a cold dark matter universe , as given by the Press-Schechter theory if an upper limit of 1-7 \times 10 ^ { 13 } M \odot is assumed on the mass of the condensations .