The fallacy of division is the mirror image of composition: it is the inference that what is true of the whole must be true of the parts. For example, the fact that my car was made by General Motors does not mean that every part was.
Consider the controversial issue of racial differences in intelligence based on IQ test scores. If such differences do exist, they are differences in the average IQ of racial groups. To infer that a given individual in one group has a higher IQ than an individual in another group, just because his or her group's average is higher, would be a fallacy of division. Averages are computed on the basis of data from individuals who are distributed along a continuum, so the group average tells us nothing about any particular individual.