Count the Fs: Why a Sample instead of a Census?
This material was originally developed through
CAUSE as part of its collaboration with the SERC Pedagogic Service.
Initial Publication Date: May 17, 2007
Summary
This interactive lecture activity motivates the need for sampling. "Why sample, why not just take a census?" Under time pressure, students count the number of times the letter F appears in a paragraph. The activity demonstrates that a census, even when it is easy to take, may not give accurate information. Under the time pressure measurement errors are more frequently made in the census rather than in a small sample.
CollapseLearning Goals
The activity motivates the need for sampling. Students learn about measurement error and that a census may not give accurate information.
Context for Use
The activity
- should be used at the beginning of the sampling discussion
- 10 minute interactive lecture
- appropriate for all levels
Teaching Materials
Handout for students handout (Microsoft Word 24kB May17 07)
Process for instructor instructor's directions (Microsoft Word 31kB May17 07)
Process for instructor instructor's directions (Microsoft Word 31kB May17 07)
Teaching Notes and Tips
Process
- Pass out the paragraph (paper blank side up) to each student asking them not to turn over the paper until signal is given.
- Explain to the students that they are to read the paragraph on the paper and count the Fs in the paragraph.
- Give students 1 minute to count the Fs. If in a computer-projector equipped classroom, bring the paragraph up on screen during this time.
- Call on one student (choose a bright one, they tend to miscount the worse, and the rest of the class will assume the bright student is correct) and ask for the count. Ask if everyone else got the same number. Then ask for show of hands for those who got 20, 25, 30, 35.
- Demonstrate the correct number by replacing all the Fs with Xs. (There are 34 Fs.)
- Discuss the measurement error that is found by asking why the students' counts were wrong. (They read over the little words containing F, for example, "of," "for")
- Explain that the Fs all look the same, aren't moving, aren't suspicious of "official" counting them, apparently want to be included in the count and the census consisted of a one minute counting activity rather than 8 hours of counting.
- Ask for possibilities of potential sampling from the paragraph to determine the number of Fs.
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Assessment
Test questions.
- Give an example of measurement error that can be found in sampling.
- Give an example of a benefit of sampling over taking a census.
- Determine sampling designs that might have given us a better estimation of the number of Fs.
