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Common Core: 7.SP.1 S.IC.1


Author: Katherine Williams

Differentiate the sample and population during sampling.

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Source: All images created by J. Gearin, except Walrus created from public domain

Video Transcription

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This tutorial covers sampling. We also talk about populations and what a sample is. Now a population we typically think of something like this, like the whole country and all the people that live inside it. But in fact, the population can be many things. It's simply the complete set of people or things being studied. It could be that standard example of all the people in the US. It could also be a class of 30 students if that's everything we're looking at, or a bowl of soup-- it could even be a thing.

Now if we're looking at a portion of that population instead of the whole thing, then we'd be looking at a sample. A sample as a subset of the population. So anything that's a smaller part of it. So instead of all the people in the US, maybe all of 50 people that we've selected randomly, or instead of a bowl of soup, just a chunk.

Now if we're doing a census, then we're obtaining data for every member of the population, so we're looking at that complete set. An advantage of the census is that it's very accurate, you're collecting data for every single person or thing in the population so that you have all that data and it's accurate. You're not taking the sample, so you're not kind of trying to extrapolate or interpolate it all. A disadvantage of doing this is the time and money that it would take.

So when you can't do a census and it's impractical, that's when you would take a sample, and sampling is the process taking a sample. So another example would be like with blood. When you are trying to obtain a sample of your blood, you're taking a smaller subset of that whole population being all the blood in your body. It isn't possible or even logical to take all of the blood out of your body, so instead you just do a sample.

Now when we're deciding between-- when we choose a census in the population, there's a lot of factors that go into play. Typically for a reminder, with a census, we're studying the whole; and with a sample, we're studying the part. So if we were looking at a tray of eight cookies and we wanted to make sure that all the cookies were delicious and good, we could do either one, because we have a pretty small set. We could do a census and eat every single cookie, every single data point-- every cookie's our data point-- each cookie is our data point-- and ensure that each cookie is not burned, that there's an equal number of chocolate chips and everything like that.

However, it doesn't really make too much sense to do a census because then we wouldn't have any cookies to share, so that might be why we want to sample. Maybe try a couple of cookies or a little bite out of each cookie. So with some things, it would make sense to do a census or a sample. With this, with a set of walruses, it is very difficult to take and measure every single walrus that's in this group, so here's where we would definitely want to do a sample. Rather than to weigh every single one of them, we weigh a small subset.

With something like this with a family and you're trying to make a decision about where to go next, you could easily do a census. You could ask every member of this family pretty easily what they would want to do next, and then you would have information on every person in the group, and it'd pretty easily be able to do a census there.

When you are taking a sample, it's important to make sure that you're doing a representative sample. So with a representative sample, the key is that the relevant characteristics of the sample are the same as the population, and all the characteristics don't have to be the same, just the relevant ones, just the major ones that you're trying to study. So let's look at a couple examples of representative and non-representative samples.

Here, we have a bowl of soup, and you can see, there's some shrimp and some vegetables and some broth, and that is our population. And we want to make sure that if we're taking a representative sample, that those relevant characteristics are the same, that there's some shrimp and some of these vegetables and some of the broth.

So here's the spoon taking our sample, and the sample that the spoon gets only has broth in it. So this is not representative. Because the spoon only has broth, it's not reflecting the fact that there's shrimp and the vegetables in the soup, so the relevant characteristics of the sample of the spoonful are not the same as the bowl. So this one is not a representative sample. If it were representative, we would want to make sure that we had some shrimp and some potatoes as well as some broth.

If we were looking at a different type of soup and we're instead looking at this one, some sort of chowder, there's a kind of creamy base, and some little flecks of vegetables and spices, the sample we're taking here is this kind of cupful. And this is a representative sample in this cupful, because the relevant characteristics of the cupful are shown-- or sorry, of the bowlful are shown in the cup. So the characteristics of the population, that creaminess and the little chunks of green, are shown in the sample. The sample has the same creaminess and the green. So here, this is a representative sample, because the relevant characteristics of the sample are the same as the population.

So this has been your tutorial on sampling.

Terms to Know

Using the entire population to obtain data


The entire set of individuals from which to sample

Representative Sample

A sample that accurately reflects the population


A subset of the population. There are many ways to select a sample.