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Can you use population to refer to a particular population? For example the population of women in Maths Class, from which we can take a sample to measure the height in order to make a judgement of the height of all the women in that class (i.e., the population).

This question is different from previous Population vs. sample questions, by addressing to the meaning and how the term "population" can be used. As I mentioned in the question: is it correct to say "population of women in Maths Class"? Or once you add some extra context to the term "population" it is no longer a population, but a sample, or something else.

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The word "population" does not refer to all living people in the world. That is the generic understanding of the word, and not the statistical understanding.

Statistically, population refers to the class/group of units (or individuals in this case) about whom you want to make some inference. If the group you want to make the inference on is "women in Math 101 in Spring 2016 at UCLA" then that is your population. You can now go ahead and gather a sample or do a census study on that population.

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    $\begingroup$ The only thing I would add to this answer is that in your example it is very clear that we are dealing with a finite population. If we are not doing a census, but we are taking a sample of known size from a finite population of a known size, then it may be appropriate to include a finite population correction. $\endgroup$
    – Dalton Hance
    Commented Mar 17, 2016 at 22:23
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You correctly distinguish in the title population from sample. Unless you gather a complete sample (eg census), then your population can only be inferred through, indeed, statistical inference from a sample.

The whole process of statistical inference rests on explicitly providing you instruments to navigate this mental voyage from your sample at hands to the population you'll never (likely) be able to appraise in full.

For instance, confidence/credible intervals tell you how much the inferential estimates you have gathered from your sample can be considered with confidence or credible.

You can find other very good takes at this issue in CrossValidated, as well as elsewhere:

What is the difference between a population and a sample?

https://en.wikipedia.org/wiki/Sampling_%28statistics%29

http://www.dissertation-statistics.com/population-sample.html

http://www.sagepub.com/sites/default/files/upm-binaries/41398_40.PDF

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    $\begingroup$ This may sound like nit-picking, but it may be important to some people and it affects how your answer might be understood: there is a sharp difference between inferring a population and inferring properties of a population. In principle, we do not infer populations: we're supposed to be able to characterize them clearly and definitively. (Otherwise, we don't really know what we're talking about.) Estimation is the process of inferring properties of a population based on properties of samples. $\endgroup$
    – whuber ♦
    Commented Mar 23, 2016 at 20:13
  • $\begingroup$ OK, every feed back is welcome $\endgroup$
    – Giuseppe Biondi-Zoccai
    Commented Mar 23, 2016 at 20:23

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