Height, Marriage, and What "Random" Would Predict
If height didn't matter at all when people paired up, the gap between husbands' and wives' heights would just follow from how tall men and women are on average. The Economist compared that "random pairing" guess to real married couples — and the two pictures don't quite match.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
If who marries whom had nothing to do with height, the difference between husbands' and wives' heights would simply reflect the two separate height distributions of men and women. The Economist compared that "random pairing" prediction with real US marriage data spanning 1999 to 2023 — and found a real, persistent gap. This idea uses that comparison to explore what a "random" baseline actually predicts, and how far reality strays from it.
Guiding Questions
- If partners paired up completely at random, what shape would you expect the "height difference" distribution to have, and why?
- Where does the actual data pull away from the "random" prediction? Read off the gap at a few different height differences and describe the pattern.
- (HL) The "expected" curve is built by combining two separate normal distributions — men's heights and women's heights. Work out its mean and standard deviation from the two originals, and check it against the chart.
- Pick another pairing you could measure this way — song lengths on a playlist, ages of siblings, anything with two linked measurements — and test whether it matches what randomness alone would predict.