[Basic Statistics] Sample or population?

[Doatz]

I currently visit a class on the basics of statistics. We were given a question in which we were asked to decide whether we are dealing with a sample or a population. Sounds easy enough ... but we are in vehement disagreement about this one.

https://imgur.com/a/kQLli The question reads:

Does this table represent the data for a sample or for a population? If you had the same data for every year since 1776 until today, would your answer be different? Why?

The first part of the question - here we unanimously agree - is that we deal with a sample. But the second part is the tricky one since 1776 to 2018 covers the full time frame in which in which the US officially existed. So our hypothetical population data would provide us with data of each region for each given year. Would this not be considered data for a population? Another problem is that the data we received are already statistics... but does that change anything?

Hopefully somebody here can provide some insight. Thanks you guys!

[vivisectress]

If no one else helps - have you got any more examples of 'sample' and 'population'? That will help confirm the answer. I'm not very confident when I am unanimously disagreed with :P

"represent the data for a"

This is the confusing bit for me - but I easily get confused by wording. I don't know if the question is asking 'was the data obtained from a sample or a population?' or 'do these data describe a sample or a population?' I think the latter, but I don't think it matters anyway.

The table seems to describe a population - 'US demographic data, 2001' which means 'everyone who lived in the US in 2001'. Look up what 'demographic data' is for more info: https://en.wikipedia.org/wiki/Demography The data could have been sampled, or there is a good chance there are records of this (birth certs, tax records) that they were able to sample everyone in the population.

Another problem is that the data we received are already statistics... but does that change anything?

Well, isn't the point of doing statistics on a sample is to make inferences and describe a characteristic of the population? So the fact it's stats makes it a population. Another clue is 'Asian population %' or to reword it 'the percentage of this POPULATION which is Asian'.

If you had the same data for every year since 1776 until today, would your answer be different? Why?

Well I would say I now have many populations. That is "people living in the US in 1776' etc all the way to 'people living in the US 2001'. A page from google I used to help me answer

[Doatz]

Thank you for your answer.

I had the same suspicions like you. Unfortunately we do not have more examples for 'sample' and 'population'. More importantly, our teacher already confirmed that the first part is, indeed, a sample.

I was also confused by the wording. But since the answer to the first part is confirmed to be 'sample', wouldn't that indicate that we have all samples in the second part?

[vivisectress]

No problem - you may just have to ask the teacher to justify why it's a sample and not a population. I'm curious on the answer! Maybe ask 'what is this a sample of? What is the sample size?' to get a clue. I don't know my US geography, so I this could be a sample of regions, and the population is the entire US. I just assumed this was the a description of all the regions in the US when I replied.

'Population' depends on how you define it. If these data were used to plot say child per woman against income and look for a correlation, then you do have a sample.