# Does assuming a normal distribution for a sample mean the sample comes from a normal distribution?

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?

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.

• 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? Oct 28 '20 at 14:53
• Your options are to: 1) proceed with the assumption 2) check if your assumption is a good one.
– Dave
Oct 28 '20 at 15:15
• I am wondering if we need a normality check if we assume the data are normally distributed. Oct 28 '20 at 15:17
• 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.
– Dave
Oct 28 '20 at 15:21

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.