Larger Populations

5 min

Teacher Prep
Setup
2 minutes of quiet work time followed by a whole-class discussion.

Narrative

The purpose of this Warm-up is for students to begin to see the need for samples of data when the population is too large. In this activity, students are asked to think about how information about an individual could be a start to estimating information about a population, but that more information should probably be collected.

Launch

Give students 2 minutes of quiet work time, and follow with a whole-class discussion.

Student Task

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

  1. How many letters are in the name you prefer to be called? How many letters are in your last name?
  2. Do the number of letters in your names give you enough information to figure out what is typical for students’ names at your school? Explain your reasoning.
  3. What might it take to figure out the typical lengths of names for all the students at your school?

Sample Response

Sample responses:

  1. preferred name: 5; last name: 8
  2. Sample response: Not really. It gives a place to start for a single possibility, but many people have longer or shorter names, and I’m not sure if the lengths of my names are typical.
  3. Get a list of everyone in the school, count how many letters there are in each person’s preferred and last names, and calculate the mean of each data set. Another idea would be to survey some of the students in the school to use their data to make an informed guess about the whole school.
Activity Synthesis (Teacher Notes)

The purpose of the discussion is to get an idea of how samples might give some information about population data.

Invite students to share whether they think the length of their names gives enough information to understand the length of names at the school. If it does not come up, note that it may not be enough to know typical values very well, but it is a start.

Ask whether knowing the lengths of all students’ names except one at the school might be enough to get an idea of what is typical. Students should begin to understand that having a group somewhere between all of the students and a single student might be enough to get an idea of typical name lengths.

Ask students whether it would be just as difficult to find typical name lengths for people all over the world. If it does not come up, point out that the larger the group a question applies to, the more difficult it gets to collect the data and compute the measures of center and variability.

Standards
Addressing
  • 7.SP.B·Draw informal comparative inferences about two populations.
  • 7.SP.B·Draw informal comparative inferences about two populations.

5 min

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