They are not statistical quantities. Variation results in a statistical distribution, usually Normal or Gaussian, represented graphically by a histogram or bell-shaped curve. Then he can add tolerances the same way he would add variations, as an estimate of the assembly variation. I have seen tolerance analysis applied to single parts to estimate the accumulation of process variation as the part is produced. For example, it could be used to estimate the accumulation from multiple passes on a lathe to predict whether there will be enough material remaining to be removed by the final cut.
Vectors represent the dimensions which contribute variation in an assembly.
Engineers generally feel comfortable with vectors and kinematic joints. The geometry is greatly reduced. Variation analysis is much simpler on a vector model. Results are obtained instantaneously, compared to waiting times of sometimes minutes by other methods. Vector models can be created graphically, without typing equations.