A systematic study of the magnetic properties of the manganites Ln(0.5)(A,A')(0.5)MnO3 (A,A'=Ba, Ca, Sr) has been carried out. The variations of T-C and T-N vs two parameters, the average size of the interpolated cations (r(A)) and the mismatch effect represented by the variance sigma(2), have been studied for the series of manganites La-0.5(A,A')(0.5)MnO3, Pr-0.5(A,A')(0.5)MnO3, Nd-0.5(A,A')(0.5)MnO3 and Sm-0.5(A,A')(0.5)MnO3 (A,A'=Ba, Ca, Sr), involving at most three different cations on the perovskite A site. The results obtained for other (Ln, Ln')(0.5)Sr0.5MnO3 (Ln, Ln'=Gd, Sm Y, Pr) have been taken into consideration. A sigma(2)-[r(A)] diagram has been established, which displays the different types of magnetic behaviors that can be exhibited by Ln(0.5)A(0.5)MnO(3) manganites, i.e., when the temperature is decreasing, either a paramagnetic (PM) to ferromagnetic (FM) transition, or PM to FM followed by FM to antiferromagnetic transitions, or a PM to weak ferromagnetic transition. (C) 1997 American Institute of Physics.