# Lesson 12

Larger Populations

### Lesson Narrative

This lesson introduces the idea of using data from a sample of a population when it is impractical or impossible to gather data from every individual in the populations under study. Students consider whether the people in their class would be an adequate sample for several different questions and associated populations (MP3). While all of the answers given in this lesson are samples and may have some benefit to them, most of them are not the best way to select samples. In the next lesson, students learn about what makes some samples more representative of a population than others. In later lessons, students explore the best ways to try to obtain such samples.

### Learning Goals

Teacher Facing

• Comprehend the terms “population” and “sample” (in spoken and written language) to refer to the whole group and a part of the group under consideration.
• Describe (orally and in writing) a sample for a given population.
• Explain (orally) that a sample may be used when it is unreasonable to gather data about an entire population.

### Student Facing

Let’s compare larger groups.

### Required Preparation

Compute the mean and MAD for the length of the preferred names (if students do not go by their first name, use their nickname, middle name, etc.). Do the same for the last names of students in the class prior to the John Jacobjingleheimerschmidt activity.

### Student Facing

• 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.

### Glossary Entries

• mean

The mean is one way to measure the center of a data set. We can think of it as a balance point. For example, for the data set 7, 9, 12, 13, 14, the mean is 11.

To find the mean, add up all the numbers in the data set. Then, divide by how many numbers there are. $$7+9+12+13+14=55$$ and $$55 \div 5 = 11$$.

The mean absolute deviation is one way to measure how spread out a data set is. Sometimes we call this the MAD. For example, for the data set 7, 9, 12, 13, 14, the MAD is 2.4. This tells us that these travel times are typically 2.4 minutes away from the mean, which is 11.

To find the MAD, add up the distance between each data point and the mean. Then, divide by how many numbers there are.

$$4+2+1+2+3=12$$ and $$12 \div 5 = 2.4$$

• median

The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.

For the data set 7, 9, 12, 13, 14, the median is 12.

For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. $$6+8=14$$ and $$14 \div 2 = 7$$.

• 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.

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