Most cells have the ability to actively move. From single-cell video recordings of moving human breast-cancer cells and algae cells, we deduced that cells with identical DNA show large differences in their motion in our PRX Life paper "Intrinsic Cell-to-cell variance from Experimental Single-Cell Motility Data", which got featured in physics magazine as "Cells show 'Personality' when they move".Cell motion patterns contain vast information that, however, is not straightforwardly usable, since randomness and measurement errors are involved. Previous extractions of single-cell parameters neglected important influences of the randomness in the cell motion, which we now show to have a huge influence on the extracted parameters. We developed a new method to analyze and describe the motion of cells on the single-cell level, that captures the randomness of the process and allows us to correctly determine the differences between individual cells and the variance within a cell population. Since the survival probability of cell colonies and also potential infection risks by pathogens both depend on the variance within a cell population, our method opens new possibilities in medicine and biology to estimate infection and survival probabilities.