# The reason for saying "5 out of 10" instead of "1 of 2"?

I'm just being curious, i have seen on some places, statistical results where they give them in form of "10 of 100.000" or "5 of every 10".

I don't have any statistical knowledge over my personal experience/reading around. But basic maths tell me that such values could be simplified as any fraction we used to do:

10 of 100.000 -> 1 of 10.000 // 5 of every 10 -> 1 of every 2.

Is there any reason not to do it?

Edit: The numbers come from, if i remember correctly:

• 10 of 100.000 people per year with some bad reaction to medication
• 5 of every 10 people who actively smokes on ¿Spain?
• It's on statistics context. Numerical notation differs on the contexts, and im trying to understand it on a specific context. I dont think its offtopic. I think its the place of stack exchange where fits better Commented Apr 28, 2015 at 10:31
• I think that it's perfectly on topic, and it's related to the likelihood function. Commented Apr 28, 2015 at 10:33

The procedures you describe are used in practice and in fact in many cases they are recommended for numerical stability of statistical estimates. Those procedures are called centering, standardization or normalization depending on procedure.

Examples:

• if your variable has some known "baseline" value, e.g. it ranges from 100 to 10.000, then you can subtract the minimum from it, so it to starts with 0,
• if your variable is continuous then you can subtract the mean, so it is "centered" at 0,
• with continuous variables you can subtract the mean and divide by the standard deviation, so to have values in so-called Z-scores (normalization),
• you can subtract min and then divide by max - min to get values in [0, 1] range,
• you can use all other kinds of transformations like squaring, square-rooting, taking logs etc.

In many cases such procedures are recommended. On another hand, taking the raw values could be helpful for making the results easier to interpret (e.g. age 45 is easier to interpret than age -5 if 50 was a "baseline" age in centered variable).

In some disciplines there are standard ways of describing some numerical values and your example is one of them, because in epidemiology it is common to report prevalence as $n$ cases per 100 000 people. It is a matter of convention.

• Added edit with where the values come from to clarify, both are about number of people Commented Apr 28, 2015 at 10:52
• It does not matter what the numbers represent, the procedures are the same for brain cells, people, particles etc.
– Tim
Commented Apr 28, 2015 at 10:53

The way you say it conveys information regarding the precision of the probability you have in mind. Saying "5 out of 10" says your margin of error is about +/- 0.05 (because you did not say "6 out of 10"). Likewise, saying "500 out of 1000" usually implies higher precision.

• 5 out of 10 is exactly the same as 500 out of 1000... There is no implication about precision in here.
– Tim
Commented Dec 20, 2015 at 9:10