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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

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Lesson Transcript

Instructor:
*Cathryn Jackson*

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

One of the most useful things we can do with data is use it to describe a population. Learn how in this lesson as we discuss the concepts of parameters and samples.

Josephina is looking to start her own small business. She wants to call her business 'Puppy Paws' and sell shoes, socks, and booties to pets of all kinds. She needs to conduct some research to find out if her business will be successful in her town. However, she does not have time or the resources to talk to everyone in the town about her business. To gather information, Josephina will need to ask a sample and infer information about the population from the sample.

In this lesson, you will learn about the relationship between population and parameters, as well as the relationship between samples and statistics. Lastly, we will use this information to learn how to infer parameters about certain populations.

To find out if her business will be successful, Josephina will need to understand the population of her town. A **population** is all members of a specified group. In this case, all of the citizens that live in Josephina's town are considered members of the target population. Josephina wants to know the mean number of pets that each person in the population owns.

When statisticians talk about mean, or average, they use the symbol called mu. Often, this mean, or average, is used to tell statisticians about the population they are studying. This is also known as a parameter. A **parameter** is a characteristic used to describe a population. Josephina needs to understand the characteristics of the population in order to understand if there is a need for her business. For example, if she finds that the pet ownership parameter of the town is .25 pets per person, then she knows that there are enough pets in the town for her business to be successful.

Now that you understand the relationship between population and parameters, let's discuss how they relate to samples and statistics.

Since Josephina can't ask everyone in the town about her business, she will need to reach out to as many people as possible. This is called a **sample**, which is a part of a population used to describe the whole group. Josephina wants to know the average number of pets per person and the interest that each person has in providing footwear for their pets. To find this information without surveying the whole town, she can take a sample in many different ways. These include: random sampling, simple random sampling, cluster sampling , stratified sampling, and systematic sampling. You'll learn more about each of these types of sampling in future lessons!

First, Josephina wants to collect information about how many pets there are in the town, so she decides to go to a gathering place in the town and ask the people there about their pets. Since the dog park would give her biased information, she decides to survey people at a local movie theater. After she collects all of the information from the movie theater, she can create a statistic. A **statistic** is the characteristics of a sample used to infer information about the population. Of the people that Josephina surveyed, one in three own at least one pet. But how can we use this information to understand the population, since it only reflects the sample? We can do this by inferring parameters from our statistics.

Inferring parameters from statistics is pretty simple in this lesson. You will just take the statistic that you've found and use it to determine the parameter. In future lessons, you will learn more about the accuracy of your parameter, which is important. For example, if Josephina surveyed the people in the dog park about the number of pets they own, she would probably find that every person owned at least one pet. But we know this is probably not an accurate way to describe the entire population. We can determine how accurate a parameter is by using a concept called a confidence interval. That's a more complicated concept that we will discuss in a future lesson. For now, let's look at parameters in a more logical fashion.

Josephina wants to know if pet owners would be interested in footwear for their pets. She surveys people at the movie theater and at the dog park. Everyone is required to answer the question, even if they don't own a pet. Considering that Josephina's population is all pet owners in the town, which piece of information should she use to develop a parameter?

Because Josephina's population is all pet owners, she needs to use the data she collected from the dog park only. Even though she found some pet owners at the movie theater earlier, remember that everyone is required to answer the question, so the people at the movie theater don't fit the population and, therefore, would not be an accurate sample. If Josephina finds that 78% of the people in the dog park would be interested in footwear for their pets, can she use this as a parameter?

What do you think? Can Josephina assume that because 78% of the people in the dog park would be interested in footwear for their pets, that 78% of the pet owner population also would be interested? This is a tricky question. Technically, the statistic 78% is an accurate sample of the population. However, other factors may need to be considered. For example, it sounds like Josephina only surveyed dog owners, but her business is for all pets. To get a more accurate parameter, Josephina may need to conduct her survey with other pet owners.

On the other hand, Josephina can get more accurate results if she surveyed people at the movie theater, asking first if they owned a pet, and then only asking the pet owners if they would be interested in footwear for their pets. When she does this, she finds that about 64% of the pet owners surveyed are interested in footwear for their pets. She can more accurately infer that 64% of the pet owners in the town would also be interested. This means that she can use the statistic, 64%, to infer the parameter, 64%.

An important part of conducting research and collecting data is using that information to develop conclusions. In this lesson, we discussed using statistics to infer parameters. First, you need to understand the relationship between population and parameters. A **population** is all members of a specified group, such as all of the pet owners in the town for Josephina's survey. A **parameter** is a characteristic used to describe a population, such as whether or not the people in Josephina's town are pet owners.

Next, you can use statistics to infer parameters about certain populations. Remember, a **sample** is a part of a population used to describe the whole group. This would be the people that Josephina surveyed in the dog park and the movie theater. We know the people in these places are probably not the only pet owners in town; however, we can say that they are members of the population, so information gathered about them can be a good sample for her research. Meanwhile, a **statistic** is the characteristics of a sample used to infer information about the population, such as the 78% of the dog park people who were interested in footwear for their pets or the 64% of the pet owners surveyed at the movie theater.

Understanding these concepts, you can analyze and infer information from the data you collect. Just make sure you are careful in analyzing where the statistic is coming from and how unbiased the sample could be. Learn more about bias in future lessons!

When you are finished, you should be able to:

- Explain what a population and a parameter are in statistics
- Understand what samples and statistics are
- List the different kinds of samples that can be used when gathering data from a population
- Describe how to infer a parameter and judge its accuracy

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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

- Descriptive & Inferential Statistics: Definition, Differences & Examples 5:11
- Difference between Populations & Samples in Statistics 3:24
- Defining the Difference between Parameters & Statistics 5:18
- Estimating a Parameter from Sample Data: Process & Examples 7:46
- What is Categorical Data? - Definition & Examples 5:25
- Discrete & Continuous Data: Definition & Examples 3:32
- Nominal, Ordinal, Interval & Ratio Measurements: Definition & Examples 8:29
- The Purpose of Statistical Models 10:20
- Experiments vs Observational Studies: Definition, Differences & Examples 6:21
- Random Selection & Random Allocation: Differences, Benefits & Examples 6:13
- Convenience Sampling in Statistics: Definition & Limitations 6:27
- How Randomized Experiments Are Designed 8:21
- Analyzing & Interpreting the Results of Randomized Experiments 4:46
- Confounding & Bias in Statistics: Definition & Examples 3:59
- Confounding Variables in Statistics: Definition & Examples 5:20
- Bias in Statistics: Definition & Examples 7:24
- Bias in Polls & Surveys: Definition, Common Sources & Examples 4:36
- Misleading Uses of Statistics 8:14
- Go to Overview of Statistics

- Go to Probability

- Go to Sampling

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