We have calculated the proton charge radius by assuming that the real proton radius is not unique and the radii are randomly distributed in a certain range. This is performed by averaging the elastic electron-proton differential cross section over the form factor cutoff. By using a dipole form factor and fitting the middle value of the cutoff to the low-Q2 Mainz data, we found the lowest χ2/N for a cutoff Λ=0.8203±0.0003 GeV, which corresponds to a proton charge radius rE=0.8333±0.0004 fm. The result is compatible with the recent precision measurement of the Lamb shift in muonic hydrogen as well as recent calculations using more sophisticated techniques. Our result indicates that the relative variation of the form factor cutoff should be around 21.5%. Based on this result we have investigated effects of the nucleon radius variation on the symmetric nuclear matter (SNM) and the neutron star matter (NSM) by considering the excluded volume effect in our calculation. The mass-radius relation of a neutron star is found to be sensitive to this variation. The nucleon effective mass in the SNM and the equation of state of both the SNM and the NSM exhibit a similar sensitivity.