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Count the Fs: Why a Sample instead of a Census?

Authored by Carolyn Cuff, Westminster College
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This activity has been undergone anonymous peer review.

This activity was anonymously reviewed by educators with appropriate statistics background according to the CAUSE review criteria for its pedagogic collection.


This page first made public: May 17, 2007

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

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.

Paragraph of text for activity

Learning 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

Description and Teaching Materials

Handout for students handout (Microsoft Word 24kB May17 07)
Process for instructor instructor's directions (Microsoft Word 31kB May17 07)

Teaching Notes and Tips

Process
  1. Pass out the paragraph (paper blank side up) to each student asking them not to turn over the paper until signal is given.
  2. Explain to the students that they are to read the paragraph on the paper and count the Fs in the paragraph.
  3. Give students 1 minute to count the Fs. If in a computer-projector equipped classroom, bring the paragraph up on screen during this time.
  4. 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.
  5. Demonstrate the correct number by replacing all the Fs with Xs. (There are 34 Fs.)
  6. 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")
  7. 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.
  8. Ask for possibilities of potential sampling from the paragraph to determine the number of Fs.
An extension, wrap up, and follow up can be found in the instructor's handout.

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.
In class question.
  • Determine sampling designs that might have given us a better estimation of the number of Fs.

References and Resources