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If I give you three numbers that are independently and identically drawn from a standard normal distribution, then have I given you three samples or one sample?
If the answer is one sample, then is there a short name for what I have given you three of?

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    $\begingroup$ One sample, three observations or data points. $\endgroup$
    – jbowman
    Jan 11 '12 at 22:02
  • $\begingroup$ Sometimes people call them three 'replications', but I prefer @jbowman's terminology. 'Cases' is also used. $\endgroup$ Jan 11 '12 at 22:09
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    $\begingroup$ jbowman is correct. Note, however, that to be effective, statisticians have to communicate clearly with people in other disciplines. In many of the natural sciences, a "sample" is a single piece of something: a sample of water, of soil, of rock, of a plant, etc. We have to be sensitive to these potential differences and define our technical terms, sometimes even adopting the terminology used in the application domain. Some people use the phrase "statistical sample" to make this distinction. $\endgroup$
    – whuber
    Jan 11 '12 at 22:18
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    $\begingroup$ I'm from one of these natural sciences (chemistry, a bit straying into biology and medicine in terms of samples [in the meaning of three]). E.g. for medical applications, a sample may also be called a specimen, whereas the case is the patient: there can be several samples/specimen of one patient. I take spectra of these (many of each specimen). I'd call the spectra observations. And each spectrum has a number of data points (variates). $\endgroup$ Apr 11 '12 at 18:41
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    $\begingroup$ @jbowman: you should turn that into an answer. $\endgroup$
    – naught101
    Oct 2 '12 at 7:02
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Sometimes I appeal to glossaries of statistics, and they usually help. Search and bookmark one you like or think it is most helpful.

For example, here are some definitions retrived from the "Glossary of Statistical Terms" from stat.berkeley.edu website.

  1. Units: a member of a population

    A unit could also be interpreted as an observation from a population.

  2. Sample: a sample is a collection of units from a population.

  3. Random sample: a random sample is a sample whose members are chosen at random from a given population in such a way that the chance of obtaining any particular sample can be computed. The number of units in the sample is called the sample size, often denoted n. The number of units in the population often is denoted N. ...

The definition of random sample continues, but here I quoted the relevant part related to the question.

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