In this activity, students are asked to compare two groups (length of preferred names and last names) by collecting data from the class. They are asked if the data from the class gives enough information to draw a conclusion about a larger group (MP3). This activity gives students the first chance to experience why sampling might be needed.

The purpose of the discussion is for students to see how the data they have might relate to a larger group. In particular, that a sample might give some estimate of a larger population, but the estimate should not be assumed to be exact.

Consider asking these questions for discussion:

• “Do you expect the mean length of first names for the school to be exactly the same as the mean length for the class?” (Probably not exactly the same. It may be close, though.)
• “Do you expect the mean length of first names for the school to be much larger or smaller or about the same as the mean length for the class? Explain your reasoning.” (Unless there are a few outliers in the class, it should be fairly close to the mean from the class.)

In this activity, students think a little more deeply about the data we would like to know and how that compares to the data we can collect easily and quickly (MP1). They are presented with a statistical question that does not have an obvious answer. Students then consider ways they might begin gathering data to answer the question, but realize that the data they could reasonably collect is not everyone addressed by the question. Following the activity, the discussion defines the term “population” as a set of people or things that is studied and the term “sample” as a part of the population from which data is actually gathered.

The purpose of the discussion is to show the difference between the data we would like to have to answer the question and the data we have available.

Define population and sample. A population is a set of people or things that are studied. In this usage, it does not have to refer only to groups of people or animals. For example, when finding the average size of a grain of sand, the population would be all the grains of sand that exist. A sample is the part of the population from which data is actually collected.

Direct students' attention to the reference created using Collect and Display. Ask students to share whether the collected words describe a population, a sample, or both. Invite students to borrow language from the display as needed, and update the reference to include additional phrases as they respond.

Ask students, 

• “What is the population for the question about stop signs?” (everyone in the world who goes to school) Note that we would need data from everyone, including those who ride as well as those who walk or bike.
• “What might be a sample we could use to answer the question?” (the students in our class, my neighbors, a few people from different countries)
• “What might be the benefits and drawbacks of each of these samples?” (Some may be more convenient but would not represent the population as well, or the other way around.)
• “What would you do with the data collected from everyone to answer the questions?” (I would find the mean and MAD of the data from the 2 sets and compare them like we did in previous lessons.)

Explain: While it is best to have data for the entire population, there are many reasons to use a sample.

• More manageable. With very large populations, the amount of data can be hard to collect and work with, so a smaller subset may still be informative and easier to work with. Example: Find the average size of a grain of sand.
• Necessary. Sometimes it is impossible to reach the entire population, so a sample is all that is available. Example: Find the average lifespan of tuna fish.
• Speed. Sometimes a rough estimate is all that is needed, and a sample of data is enough to estimate the population characteristic. Example: Find the median number of apps on smartphones.
• Cost. Sometimes it is very costly to obtain the data needed, so a sample can reduce the cost. Example: Find the average amount of hydrogen in moon rocks.

This activity gives students the opportunity to practice the new vocabulary of population and sample by identifying the population from a set of questions and describing a possible sample that could be used to get some information to begin answering the question. Since each of these words has a very specific meaning in the context of statistics that is different from the colloquial use of the word, it is important for students to work with the vocabulary word in specific situations to understand its meaning (MP6).

The purpose of the discussion is to further solidify the meaning of the terms “population” and “sample” for students.

Consider asking these questions for discussion:

• “For each question, could there be another population than the one you gave?” (No. The population refers to all of the individuals that pertain to the question.)
• “For each question, could there be another sample than the one you gave?” (Yes. A sample refers to a few of the individuals from whom data will be collected and does not specify the number or how the individuals are selected.)
• “What are some of the advantages and disadvantages you determined for the samples you chose?” (Some are easy to work with, but might miss large sections of the population.)
• “What is a question you could ask for which the population would be all of the books in your house?” (“What is the average number of pages in books in my house?”)
• “What is a question you could ask for which the sample could be all of the books in your house?” (“What is the average number of pages in all the books ever written?”)

Explain that a well-phrased question should only have 1 population (a question that is not well-phrased should be reconsidered so that the purpose of the question is clear), but there are usually many ways to find samples within that population.