Why Inferential Statistics?
Imagine we had a question: “Do men and women differ on X?”
No matter what “X” is—height, empathy, knowledge of 13th century Spanish history, or anything else—we know that any given man will be different than any given woman, but what we don’t know is how men “on average” differ from women “on average.” That is, when we asked our initial question, we probably wanted to know how the mean for men compared with the mean for women. But we will never know the actual mean for men or the actual mean for women, because that would involve measuring more than 7 billion people! So, we need to, somehow, get a sample of men and a sample of women, compare them, and draw a conclusion from that.