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As my question says, I am wondering what people mean when they say the data follows a normal distribution, does this mean the population follows a normal distribution?

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A sample can’t be normal!

Samples are necessarily finite. A normal distribution can take on infinitely many values, so a sample can’t be normal.

Therefore, when we say that we have points that are distributed normally, we mean that they come from a normal population.

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  • $\begingroup$ If we assume that the data is normally distributed meaning the data come from a normal distribution, then do we need to perform the normality check? $\endgroup$ – StoryMay Oct 28 '20 at 14:53
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    $\begingroup$ Your options are to: 1) proceed with the assumption 2) check if your assumption is a good one. $\endgroup$ – Dave Oct 28 '20 at 15:15
  • $\begingroup$ I am wondering if we need a normality check if we assume the data are normally distributed. $\endgroup$ – StoryMay Oct 28 '20 at 15:17
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    $\begingroup$ I would like to check if my assumption is a reasonable one. // You're still learning, so please be careful with terminology so you know what's really happening. The data can't be normal; the data could be drawn from a normal population distribution, however. $\endgroup$ – Dave Oct 28 '20 at 15:21
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It is hard to guess, where your problem lies, but it seems to me that you have not yet grasped the concept of a sample. The statistical model underlying this concept is as follows:

  1. A numeric result of a random experiment follows a certain probability distribution.
  2. The random experiment is repeated independently $n$ times
  3. The list of results $x_1,\ldots,x_n$ is called a "sample".

The distribution in 1. can be a normal distribution, which is the case to which you refer.

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