~ 8.12 ~

Larger Populations

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Learning Targets

I can explain why it may be useful to gather data on a sample of a population.
When I read or hear a statistical question, I can name the population of interest and give an example of a sample for that population.

Notes

A population is a set of people or things that we want to study. Here are some examples of populations:

All people in the world
All seventh graders at a school
All apples grown in the U.S.

A sample is a subset of a population. Here are some examples of samples from the listed populations:

The leaders of each country
The seventh graders who are in band
The apples in the school cafeteria

When we want to know more about a population but it is not feasible to collect data from everyone in the population, we often collect data from a sample. In the lessons that follow, we will learn more about how to pick a sample that can help answer questions about the entire population.

Vocabulary

population

A population is a set of people or things that we want to study.

For example, if we want to study the heights of people on different sports teams, the population would be all the people on the teams.

sample

A sample is part of a population. For example, a population could be all the seventh grade students at one school. One sample of that population is all the seventh grade students who are in band.

Activities

12.2 John Jacob Jingleheimer Schmidt

7th Grade Class Roster

In general, do the students at this school have more letters in their first name or last name? How many more letters?

How many letters are in your first name? In your last name?
Do the number of letters in your own first and last names give you enough information to make conclusions about students' names in your entire school? Explain your reasoning.
Your teacher will provide you with data from the class. Record the mean number of letters as well as the mean absolute deviation for each data set.
Which mean is larger? By how much? What does this difference tell you about the situation?
Do the mean numbers of letters in the first and last names for everyone in your class give you enough information to make conclusions about students’ names in your entire school? Explain your reasoning.

12.3 Siblings and Pets

Consider the question: Do people who are the only child have more pets?

Earlier, we used information about the people in your class to answer a question about the entire school. Would surveying only the people in your class give you enough information to answer this new question? Explain your reasoning.
If you had to have an answer to this question by the end of class today, how would you gather data to answer the question?
If you could come back tomorrow with your answer to this question, how would you gather data to answer the question?
If someone else in the class came back tomorrow with an answer that was different than yours, what would that mean? How would you determine which answer was better?

12.4 Sampling the Population

For each question, identify the population and a possible sample.

What is the mean number of pages for novels that were on the best seller list in the 1990s?
What fraction of new cars sold between August 2010 and October 2016 were built in the United States?
What is the median income for teachers in North America?
What is the average lifespan of Tasmanian devils?

Add to Your Notes

While it’s best to have data for the entire population, there are many reasons to use a sample.

more manageable (find the average size of a grain of sand)
necessary (find the average lifespan of tuna)
speed (find the median number of apps on smartphones)
cost (find the average amount of hydrogen on moonrocks)

What are some drawbacks of using samples instead of the entire population?

The value of center will not be exact. Some groups may not have been included in the sample.

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