Let's say there are 10 points on a plane, and I'd like to describe their distribution as homogeneous. Which of the following is correct?

  1. The point distribution is homogeneous.
  2. The points distribution is homogeneous.
  3. The points' distribution is homogeneous.

I have heard the 1st a lot. I tend to use the 3rd as it sounds more logical to me to maintain both the plurality of the points and to use a genitive, but I have the feeling the 2nd is correct when I rephrase it using 'people' instead of 'points'. In that case the choice would be between

  1. The person distribution is homogeneous.
  2. The people distribution is homogeneous.
  3. The people's distribution is homogeneous.

What is the correct way to say it? Thank you.

Edit: it's been pointed out that this question is in matter the same as "A mice problem" vs. "a mouse problem". But I believe my doubt goes beyond the choice between single and plural attributive noun.

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    I like this question. The first set seems simple; point is using the noun attributively, points' is a correctly used plural genitive, and points looks a bit off. But your people example behaves differently. – oerkelens Jun 9 '15 at 7:57
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    The 'singular or plural attributive noun' question is answered at "A mice problem" vs. "a mouse problem" (in a nutshell, singular attributives are more common, but plural ones are available on logical grounds). The 'attributive noun vs genitive structure' query is answered in another question. – Edwin Ashworth Jun 9 '15 at 9:25
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    As a mathematician I would read the 1st and 3rd statements at least somewhat differently. The 1st statement would indicate that i have an actual distribution (in the meaning of the word as used in probability) for one or more points. I might not even have any points currently I might just know that whenever they might be used the distribution according to which they appear (are observed) will be homogenous. In the 3rd sentence to me it sounds a lot more as if I actually have some set of points (probably in some n-dimensional space) which are homogeneously distributed (in that same space). – DRF Jun 9 '15 at 11:19
  • @EdwinAshworth I have the feeling there a difference with the mouse/mice case you cite. To use another example, let's take a strange table with 10 legs. We'd all speak about the table leg but how would you speak about their spacing? Would you still consider correct to say leg spacing or you'd have to switch to plural with genitive, legs' spacing? – raggot Jun 9 '15 at 11:38
  • @DRF There's where I come too. But still let's assume a sociologist is analysing the behaviour of 10 people in a room. Then they might speak about their distribution in space. As odd as it can sound... If a person and a point are equivalent for the hypothetical sociologist, then my question remains valid – raggot Jun 9 '15 at 11:42

How about "distribution of points" for clarity?

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    A good suggestion, but it does not really answer the question. – Drew Jun 11 '15 at 3:13
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    I'm hoping it gets at the intention behind the question, which seems to be "How do I say this in a way that is clearly grammatically correct, which cannot be criticized on grammatical grounds?" – WBT Jun 11 '15 at 12:33
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    @WBT Thanks, but Drew is right. The origin of my question is a dispute between colleagues. And the stakes are high :) – raggot Jun 11 '15 at 12:44
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    Well, maybe it'll be helpful for somebody else who's doing comes across this question after a search with the intention I noted. – WBT Jun 11 '15 at 12:49
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    @WBT: The proper way to offer it as helpful info that is not an answer is to make it a comment to the question. Yes, comments can be helpful. They just are not answers to the question. – Drew Jun 11 '15 at 14:02

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