# Drwaing the probability distribution of the population from a sample

#### SWDave

##### New Member
Hey there,

this might be a bit of an uneducated question, but I want to make sure I don't get anything wrong.

I'm wondering if one can draw conclusions regarding probability/frequency distribution/density of a population from a sample. I often see descriptive patterns in research papers concluding that a variable X distributes in some way regarding the manifestation of a variable y (e.g. companies raise either the money needed [100%] or barley anything from investors[0-5%]). They show this in some ordinary two dimensional coordinate system and assume this holds true in general (and thus the whole population).

1. Now, since descriptive statements only hold true for a sample, shouldn't the above be an invalid conclusion?
2. And if so, how does one derive the true probability/frequency distribution/density of a population from a sample?

#### BGM

##### TS Contributor
This question related to philosophy of statistics; I try my best to explain a little bit.

Unless you are doing some kind of census, most of time people will not have the complete information of the whole population due to time/money/other physical constraints etc. The good thing of statistics is that even we only observe just a part of the whole population, we make use of this information and have a statistical inference on it. Therefore, as you mentioned, the estimate will never be 100% accurate, and we will live with the errors. And statistics try to model those errors (not unmanageable) and usually will desire a property that those errors will vanish as you have sufficiently large sample size. Of course as most of the other science subjects, we have make some assumptions behind as well.

For the second question, I would say you maybe looking for something like Empirical Cumulative Distribution Function (ECDF), but not sure as the passage you post seems mentioning some bivariate relationship which like a regression model.