It works the same way as any other time a sentence like "A has a greater value in X than B, C and D combined" appears
-- to illustrate that A is significantly larger compared to its siblings in the set and its usually meant to be a surprising fact.
X can be a total, per capita or some other rate or whatever, it will depend on the context, as long as it's the same, it doesn't the affect the intent of the sentence.
To expand it further. I assume you don't consider below being misleading somehow:
Mary gets paid 90k per annum -- which is more than what both Jane and Jill receive per annum combined.
It's the same principle.
I guess I see now where confusion point seems for other people.
> If it's per capita, can't you just list every city that has a lower per-capita rate and claim that it is higher than all of them "combined"?
I can't, since that would be wrong, that basically not how I ever read and understand that sentence(if it has "combined" in it), I am not a native english speaker so I'm maybe wrong on this.
Mary gets paid 90k per annum, this is more than what Jane and Jill get per annum combined. I read it as:
Mary's per annum (90k) > Jane's per annum + Jill's per annum
Mary gets paid 90k per annum, this is more than what Jane and Jill get per annum. I read it as two separate comparisons:
Mary's per annum (90k) > Jane's per annum,
Mary's per annum (90k) > Jill's per annum
Salary per annum combines additively, that's fine. £10/yr + £20/yr = £30/yr, easy.
When you add 2 annual salaries you're not increasing the number of years that the salary is paid over.
Death rate per capita does not combine additively, that makes no sense. What would it even mean? 0.1 deaths per capita + 0.2 deaths per capita is not equal to 0.3 deaths per capita because the denominator changes.
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.
Are you saying that if Chicago,LA,NYC have death rates of 23.14,7.01,3.39 per 100k, then the combined death rate of Chicago, LA, and NYC is 23.14 + 7.01 + 3.39 = 33.54 per 100k?
If that's what you're saying, then you're wrong, because the combined death rate of 3 cities would be the number of deaths across 3 cities divided by the number of people across 3 cities. It would not be the number of deaths per 100k in each city added together!
If that's not what you're saying, then I don't understand how it can be meaningful to compare those figures.
"Combined" is AFAIK not well defined. You are taking it as the (weighted) average, while I'm taking it as the sum.
As which of the two you take it is obviously very context dependent. If someone would ask you what the combined output of two factories per hour is, would you tell them the average?
I think it's a very meaningful comparison, as it highlights that there is a severely increased risk of dying of murder in Detroit. To put the same in a different framing: You could live one year in Chicago, one year in LA, one year in NYC and run a lower risk of being murdered than if you were living in Detroit for just one year. Of course this is just one small piece in the overall puzzle of mortality statistics, and might not have a big impact even at elevated levels, but that's a different topic.
Such "combined number of second, third, ... places" (= sum) figures are good at quickly highlighting that there must be something out of the ordinary happening, because a smallish deviation of a few percent can not be expressed as a sum of e.g. second and third place. There are of course some other problems with this method of comparing figures (e.g. bias - as a foreigner, I would have assumed a much higher murder rate for NYC), but there is nothing inherently wrong with comparing numbers this way.
The comparison with time is totally bogus because the amount of time does not change as you add more cities/factories.
If someone asked you the combined output of two factories per worker, would you tell them the sum?!
If the first factory produces 1 item per hour and the second factory produces 1 item per hour, then combined they are producing 2 items per hour. Agreed.
If the first factory produces 5 items with 1 worker and the second factory produces 5 items with 1 worker, then combined they're producing 5 items per worker, not 10 items per worker!
> The comparison with time is totally bogus because the amount of time does not change as you add more cities/factories.
But it does (when we are summing over the time axis)! We always had time built into the unit (deaths/100k people/year), so of course it makes sense to look at it in the context of time by applying specific values for them.
> If someone asked you the combined output of two factories per worker, would you tell them the sum?!
With that specific vague query, I'd probably ask a follow up question, as I assume that the person asking the question doesn't exactly know how to interpret the number, which is often the case if someone asks for "combined" and "per" in the same sentence. I've helped people build enough BI dashboards to spot when people try to avoid thinking about the data implications behind the operations they think they want to do, and "combine" is one of the top keywords for that.
> If the first factory produces 5 items with 1 worker and the second factory produces 5 items with 1 worker, then combined they're producing 5 items per worker, not 10 items per worker!
Factory 1 is producing 5 items/worker/hour, just as factory 2 is, so "combined" they are producing 10 items/hour, which is just as valid as your statement. As long as you are mindful with the units and the context, either way is fine.
To expand it further. I assume you don't consider below being misleading somehow:
Mary gets paid 90k per annum -- which is more than what both Jane and Jill receive per annum combined. It's the same principle.