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And it is normally per 100,000 people.
Of course. But not (necessarily) of the entire country. And it is debatable whether it makes sense to even adjust it for the population of one city / area at the start, as the infection will just spread unhindered either way, and for the spread (and therefore to assess the virulence etc.) it doesn't matter much whether beyond the people infected, there are 1 million more or 10 million more - that's not the limiting factor at the beginning. As the whole thing matures, it starts to make more sense to look at it as a spread in a certain group of people of course, be it a city or a province or a state or whatever.
But if you do that too early, all you do is just make the infected percentage look ridiculously small and barely noticeable, which doesn't show the seriousness of the situation well.
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https://www.worldometers.info/coronavirus/
You can sort for deaths per 1 million population here.
It would pick an appropriate population right?
You might say:
The rate in London is 5 per 1,000,000 people
Which would mean 40 people (ISH)
In Wuhan it's 6 per 1,000,000
At some point you're going to start using a rate of something. And it is normally per 100,000 people.