Translation of "count proportion" and "continuous proportion"

Question

I would like to know how to translate the terms count proportion and continuous proportion into German. I illustrate what I mean by these terms by means of two examples:

Count proportion
Suppose I toss a coin b times. The number of resulting heads is a. Then the quotient a /b is a count proportion.

Continuous proportion
Let d be a volume of beer and let c be the volume of alcohol that the beer contains. Then the quotient c /d is a continuous proportion (and in this case has its own name).

Examples of real-life usage
This answer and this answer.

Answer 1

The fitting translation for proportion is Anteil in this case, see e.g. Linguee.

I don't think that there are established special terms for "count proportion" and "continuous proportion" in German.

Something that is used is the term zahlenmäßiger Anteil, in the sense of: you have a crate full of apples and oranges, and you can count fruits to get the zahlenmäßiger Anteil of apples, or you can weigh them or measure their volume to get the Gewichtsanteil or Volumenanteil. IMHO this might be a good fit for "count proportion", too.

A different way to approach this would be to look at the terms that are used for variables in general in statistics, which leads to diskrete vs. stetige (or: kontinuierliche) Merkmale/Variablen:

An explanation can be found e.g. here or in any basic statistics text.

Transfering this to proportions, the terms would translate to diskreter Anteil and stetiger Anteil. You can definitely use these and they make sense. Conceptually, the term diskret (discrete) is quite far away from count though.

Answer 2

The latter one is easier to answer and I would go with

Kontinuierliches Verhältnis

Sei d das Volumen eines Bieres und c das Volumen des im Bier enthaltenen Alkohols. Der Quotient c/d wird dann als kontinuierliches Verhältnis bezeichnet.

The first case is a bit more tricky. There is Zahlenverhältnis which literally means the relation of proportion between to numbers. However if you're counting something I'd go with Zählverhältnis. I didn't have any statistics class in German so I don't know if there's an established terminology. Possibly, the English expression is used verbatim in German.

Sei b die Anzahl an Münzwürfen und a die dabei erhaltene Anzahl des Ereignisses "Kopf". Der Quotient a/b wird dann als Zählverhältnis bezeichnet.

The terms I'm familiar with are diskrete und kontinuierliche Wahrscheinlichkeitsverteilungen. However strictly speaking, this only works with proportions for large numbers.

Answer 3

In my opinion, the word Verhältnis would do in both cases. I have never heard of special terms for this distinction, and frankly speaking, I doubt that it is used in English.