The denominator changes because when you look at 2 cities together you don't just add the deaths (numerator), you also add the entire population (denominator).

The denominator changes because when you look at 2 cities together you don't just add the deaths (numerator), you also add the entire population (denominator). If there are 100,000 people in city 1, with 5 deaths, and 100,000 people in city 2, with 10 deaths, then we have: city 1: 5 deaths per 100,000 city 2: 10 deaths per 100,000 Adding them together, we don't get 15 deaths per 100,000! We get 15 deaths per 200,000 (because they each have 100k residents) = 7.5 deaths per 100,000. I feel like I'm missing the joke here. EDIT: I mean, yeah, literally, if you add the fractions together, you get what you wrote. But that's not a meaningful way to combine death rates.