sample and population (set or collection)

Question

In my Statistics class they introduced a population as the set of all measurements of interest to the investigator(e.g. height of humans) and a sample as a subset of the measurements selected from the population of interest from the population of interest; however, are these not just collections and a part of a collection as there can be many pieces of data that are the same(same heights)?

What do you call a smaller portion of a collection?

Thanks

Answer 1

I think your class is mixing up two concepts:

1. Sample space of the experiment: E.g., all adults in the US
2. Sample space of a random variable: E.g. the height of a selected adult from (1).

When talking about sets/subsets, you really can only apply that to (1). A sample from the population of all US adults is a subset all all US adults. However, the heights of each person in the sample does not constitute a subset, because you can have duplicates measurements.

Just think Population and sample - forget all that set/subset stuff -- unnecessary abstraction for intro stats.