More about Sampling Variability

10 min

Teacher Prep
Setup
Groups of 2 different from the Reaction Times activity. 2 minutes quiet work time followed by partner work time and whole-class discussion.

Narrative

Students calculate the mean of a sample collected in an earlier lesson to compare with their partners. Students experience firsthand that different samples from the same population can produce different results. In later activities students will use the data they have collected here to develop a deeper understanding of sampling variability.

Launch

Arrange students in groups of 2 so that different partners are used from the ones used in the earlier activity analyzing reaction times of 12th graders for a track meet.

Remind students that the numbers came from a survey of all 120 seniors from a certain school. The numbers represent their reaction time in seconds during an activity in which they clicked a button as soon as they noticed that a square changed color. Those 120 values are the population for this activity.

Give students 2 minutes of quiet work time followed by partner work time. Follow with a whole-class discussion.

Student Task

Earlier, you worked with the reaction times of twelfth graders to see if they were fast enough to help out at the track meet. Look back at the sample you collected.

  1. Calculate the mean reaction time for your sample.
  2. Did you and your partner get the same sample mean? Explain why or why not.

Sample Response

Sample responses:

  1. 0.43 seconds
  2. The two means were slightly different, but both close to 0.43 seconds. Because there are different samples, the means are slightly different.
Activity Synthesis (Teacher Notes)

The purpose of the discussion is for students to think about how the data they collected relates to the population data.

Some questions for discussion:

  • “Based on the information you currently know, estimate the mean of the population. Explain your reasoning.” (Since both my partner and I got means close to 0.4, I think the population mean will be a little greater than 0.4.)
  • “If each person selected 40 reaction times for their sample instead of 20, do you think this would provide a better estimate for the population mean?” (Since the sampling method is random, and thus fair, it should produce a better estimate.)
Standards
Building On
  • 6.SP.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
  • 6.SP.A.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
Building Toward
  • 7.SP.2·Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. <em>For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.</em>
  • 7.SP.A.2·Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. <span>For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.</span>

15 min

10 min