In this video, we are going to look at samples and surveys. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

First, let’s identify a population. A population is a total group of something that we are going to analyze. For example, if we wanted to see where the high school seniors want to go on a school trip, then the population is high school seniors. Instead of asking every single high school senior, we only want to look at part of the group. This part of the group is called a sample. It would be much easier and more efficient to only interview a percent of the high school seniors. We can safely assume that the opinions of this percentage can represent the high school seniors as a whole if we pick the sample wisely.

Now we will talk about a bias. Different groups of people can have different opinions. If you want a good representation of a group, you want to make sure that you cover the entire group, and not just certain sectors of the group.

For example, going back to the high school trip, if you ask the football team where to go on the trip, it would make sense that they would want to see a football game. If you ask the students in the theater where they want to go, it would make sense for them to want to see a play. You don’t want to focus the sample on just one group of people. It should represent the entire population. In order to do this, you would want to do random sampling. For example, you might want to ask every fifth student who enters school. You do not want to just ask the students at the gym, or at the library, or in a theater. Not every student may go to the gym, or be in the library, or be in a theater, but every student must enter school, so this method would best represent the population as a whole.

## Examples of Samples and Surveys

### Example 1

Jenna put the names of all the $6$ pets at the pound into a box. Then, she drew 6 names out of the box.

No, it is not a biased sample. Since every name had an equal chance of being drawn from the box.

### Example 2

Ruth surveyed the $200$ employees at the company who worked in Sales. Is this sample of the employees at the company in general likely to be biased?

Yes, it is a biased sample. Since the Sales employees might not be similar to the other employees.

## Video-Lesson Transcript

Let’s go over samples and surveys.

First, what is a sample?

Before we identify the sample, we have to identify the population.

A population is a total group of people or whatever it is that we are looking at what we want to analyze.

For example, we have high school seniors and we want to know where do they want to go for their school trip.

The population here is the high school seniors.

But if we want to have an idea of where do they want to go, we don’t want to interview all of them.

What we want to do is to interview a part of them or a part of the population.

This part of the population is the sample.

It will be a lot easier and efficient if we can do $10\%$ of everybody.

If we pick the group nicely, we can assume that that $10\%$ will share the same opinion with the entire population of high school senior students.

It’s very important to pick the sample wisely.

Another example.

Let’s say you are writing for a fitness blog and you’re thinking what article be best to write next.

In order to do that, you should know what the readers like.

The entire population that you’re concerned with is the readers of the blog.

But the readers vary greatly day-to-day from a hundred to ten thousand.

You don’t want to interview every single person because it might be annoying to them and it might also be too much data for you.

So, you just have to take a part of the population of readers to be your sample.

But again, you want to make sure to choose your sample wisely in order to get a good representation of all the readers.

Now, let’s go to something we call bias.

Different groups of people tend to have different opinions just like individuals have different opinions.

If you want to make a good representation of the population, you want to make sure that you cover the entire population not just sectors of the group.

For example, the high school trip.

It will make sense that if you ask the football team where they want to go, they might say a football game.

If you ask students in the theater where they want to go, they may say a play.

And other groups have different opinions.

So, you don’t want to focus your sample on just one type of group of people.

The sample should represent the entire population.

We don’t want to interview all the students. But we want to represent everyone in the population.

How do we do that?

We’ll do a random sampling.

Maybe every fifth student who enters school.

You don’t want to ask students at the gym. You don’t want to ask students at the library. Don’t ask students in theater.

But every student who enters school. Here, you will have a varied random sampling of students.

Not every student goes to the gym, or in the library, or in the theater.

If you choose something that every student takes part in such as entering school or entering the cafeteria, that will be a random sampling.

Now, let’s do the same thing for your blog.

Do you want to know what will be your next fitness article?

The population is everyone who visits the blog.

If you have a yoga section, readers are interested in yoga only.

If you have a weightlifting section, readers are biased towards that topic.

Readers on eating well section will be interested in this types of articles.

But since you want to get the opinion of all people who read your blog, it will be the best to have a survey on the main page.

This way no bias is built in.

Anybody could be on the main page. Not only readers who are interested in yoga, weightlifting, and eating well.

This survey can show up for only a couple of hours. Maybe it can show up to every other visitor. Or maybe it can be on at five minutes at a time at random parts of the day.

In this way, you cover everyone who goes to the blog without actually interviewing every single person.