# Why do demographers give rates per 100,000 people?

It seems universal that demographic statistics are given in terms of 100,000 population per year. For instance, suicide rates, homicide rates, disability-adjusted life year, the list goes on. Why?

If we were talking about chemistry, parts per million (ppm) is common. Why is the act of counting people looked at fundamentally differently. The number of 100,000 has no basis in the SI system, and as far as I can tell, it has no empirical basis at all, except a weak relation to a percentage. A count per 100,000 could be construed as a mili-percent, m%. I thought that might get some groans.

Is this a historical artifact? Or is there any argument to defend the unit?

• For homicide rates, 100,000 is essentially the smallest number needed to not report the rate in decimals. Jul 8, 2011 at 16:37
• @Andy Well I agree with that and had the same thought myself. But that leaves plenty others with rates of 1000s, because no matter how you slice it, the range of demographic info presented in the format has some orders of magnitude difference. The other argument, that 100,000 is a mid-sized city seems to be a very distinct reason. Jul 8, 2011 at 17:02
• I have never heard the mid size city scenario as a reasoning for the crime rates. Here in the US, the UCR reports crime rates for police jurisdictions, counties, states, larger regions, rural/urban, and various breakdowns by city size or metropolitan statistical areas. The town I grew up in had a population of approximately 2000 people, am I supposed to interpret the crime rate per 100,000 in my hometown as if it were a city of sized 100,000? Jul 8, 2011 at 17:52

A little research shows first that demographers (and others, such as epidemiologists, who report rates of events in human populations) do not "universally" use 100,000 as the denominator. Indeed, Googling "demography 100000" or related searches seems to turn up as many documents using 1000 for the denominator as 100,000. An example is the Population Reference Bureau's Glossary of Demographic Terms, which consistently uses 1000.

Looking around in the writings of early epidemiologists and demographers shows that the early ones (such as John Graunt and William Petty, contributors to the early London Bills of Mortality, 1662) did not even normalize their statistics: they reported raw counts within particular administrative units (such as the city of London) during given time periods (such as one year or seven years).

The seminal epidemiologist John Snow (1853) produced tables normalized to 100,000 but discussed rates per 10,000. This suggests that the denominator in the tables was chosen according to the number of significant figures available and adjusted to make all entries integral.

Such conventions were common in mathematical tables going at least as far back as John Napier's book of logarithms (c. 1600), which expressed its values per 10,000,000 to achieve seven digit precision for values in the range $[0,1]$. (Decimal notation was apparently so recent that he felt obliged to explain his notation in the book!) Thus one would expect that typically denominators have been selected to reflect the precision with which data are reported and to avoid decimals.

A modern example of consistent use of rescaling by powers of ten to achieve manageable integral values in datasets is provided by John Tukey's classic text, EDA (1977). He emphasizes that data analysts should feel free to rescale (and, more generally, nonlinearly re-express) data to make them more suitable for analysis and easier to manage.

I therefore doubt speculations, however natural and appealing they may be, that a denominator of 100,000 historically originated with any particular human scale such as a "small to medium city" (which before the 20th century would have had fewer than 10,000 people anyway and far fewer than 100,000).

I seem to recall, in a Population Geography course a few decades back, that our instructor (Professor Brigitte Waldorf, now at Purdue University) said [something to the effect] that we express the number of occurrences (e.g., deaths, births) per 100,000 because even if there are only 30 or 50 occurrences, we don't have to resort to pesky percentages. Intuitively it makes more sense to most people (though probably not readers of this esteemed forum) to say, well in Upper Otters' Bottom, the death rate from snake bite for males aged 35 to 39 in 2010 was 13 per 100,000 inhabitants. It just makes it easy to compare rates across locations and cohorts (though so too would percentages).

While I'm not a demographer, I've never heard anyone make reference to the medium-sized city argument, though it does sound reasonable. It is just that in circa 20 years of dealing with geographers and related social scientists as an undergraduate student, graduate student and now faculty member, I've never heard that particular explanation about city-size invoked. Until now.

Generally we are trying to convey information to actual people, so using a number that is meaningful to people is useful. 100,000 people is the size of a small to medium city which is easy to think about.

• Makes sense, but do you have a reference for this?
– whuber
Jul 8, 2011 at 16:42

Relative frequencies are often used to inform the general population instead of experts and they have some advantages for this use case:

• relative frequencies always allow for integers instead of fractions, which is useful if the variable of interest only makes sense in integer format (e.g. 0.5 out of 100 humans or 0.3 out of 100 births is not helpful). If the occurrence is very low (say 1 in a million), percentages are also not pretty (0.0001%)
• relative frequencies might be easier to visualize: 1 in 10 may make us think of 10 people we know; 10% is rather abstract. As Greg Snow pointed out, relative frequencies have a relation to the real world. If 100 000 people live in my city, 85/100 000 is easier to grasp.
• there is actually also scientific theory about this, the "frequency format hypothesis": "The frequency format hypothesis is the idea that the brain understands and processes information better when presented in frequency formats rather than a numerical or probability format." (from Wikipedia)
• and, finally, percentages are sometimes given without a reference class (% of what?)

There reslly is no intelligent or rational reason to convert to per 100,000.

Its just changing the units of a ratio.

The bigger probem is that most people use the wrong domain when cobverting to 100,000

There is just no good reason to do this.

• Welcome to Stats.SE. Can you please edit your post and justify your statements? It will be interesting if you can provide some references, in particular to your third sentence. While you're at it, you may correct the typos in your post. By the way, take the opportunity to take the tour( stats.stackexchange.com/tour), if you haven't done it already. See also some tips on formatting help and write down equations using LaTeX / MathJax. Aug 4, 2019 at 12:36