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I want to know whether a noun after "distribution of" should be plural or singular. For example,

The distribution of height

The distribution of heights

It is possible that "height" is not a good example of countable noun. I am not interested in the specific example. To form a distribution, there should be multiple things, so intuitively, it should be plural to me. For the above example, I see many use "height" rather than "heights" and I want some explanation for that too. Please also consider below.

The distribution of height measurement

The distribution of height measurements

  • As you said, "height" is not a good example of countable noun. Suppose you use another noun which takes the usual plural, say rat. Then it is easy to see that "The distribution of rat" is wrong. – Weather Vane Jan 4 '18 at 1:29
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Whatever follows "distribution of" must have a meaning of plural, or must be uncountable.

  • The distribution of water

  • The distribution of money

  • The distribution of the cats population

The explanation: you cannot really "distribute" one piece of something.

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If you are talking about a sample set with a finite number of discrete measurements then you definitely should use the plural.

If you are talking about the population distribution which is effectively continuous, you are better to use the singular but the plural is probably still acceptable.

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