Suppose that you and I are eating lunch in our college’s dining hall. We are talking about the heights of people. A newly hired colleague sits down with us and joins our conversation. This is our first conversation with our new colleague. Our new colleague offers an opinion: “Men are taller than women.”
Would any of us object? Take offense? See malice motivating the speaker’s words?
Or would we not credit our new friend with knowing that there many individual women who are taller than many individual men?
Our differences have a statistical nature. Men are not uniformly taller than women. However, the fraction of men who stand over six feet tall differs from the fraction of women who are so tall. The fraction of men who are shorter than five and a half feet tall differs from the fraction of women whose height is less than five and half a feet tall. The mean value of the heights of men differs from the mean value of the heights of women.
Many people count tallness among the attributes that contribute to attractiveness. Do we not all know homely tall people and handsome short people? Does anyone believe that all tall people are better than all short people?
Compare any two groups of people in any way and we are likely to see difference. We are unlikely to find that all values that we measure in one group are higher than all values in the other group. Instead, we are likely to find distinct but largely overlapping distributions of values.