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Lab 1: Central Limit Theorem (Pocket Change)

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Class Time:

Names:

Student Learning Outcomes:

  • The student will demonstrate and compare properties of the Central Limit Theorem.

Note:

This lab works best when sampling from several classes and combining data.

Collect the Data

  1. 1. Count the change in your pocket. (Do not include bills.)
  2. 2. Randomly survey 30 classmates. Record the values of the change.
    Table 1
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
  3. 3. Construct a histogram. Make 5 - 6 intervals. Sketch the graph using a ruler and pencil. Scale the axes.
    Figure 1
    Blank graph with frequency on the vertical axis and value of the change on the horizontal axis.
  4. 4. Calculate the following (n=1n=1; surveying one person at a time):
    • a. x¯ x =
    • b. ss =
  5. 5. Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Collecting Averages of Pairs

Repeat steps 1 - 5 (of the section above titled "Collect the Data") with one exception. Instead of recording the change of 30 classmates, record the average change of 30 pairs.

  1. 1. Randomly survey 30 pairs of classmates. Record the values of the average of their change.
    Table 2
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
  2. 2. Construct a histogram. Scale the axes using the same scaling you did for the section titled "Collecting the Data". Sketch the graph using a ruler and a pencil.
    Figure 2
    Blank graph with frequency on the vertical axis and value of the change on the horizontal axis.
  3. 3. Calculate the following (n=2n=2; surveying two people at a time):
    • a. x¯ x =
    • b. ss =
  4. 4. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Collecting Averages of Groups of Five

Repeat steps 1 – 5 (of the section titled "Collect the Data") with one exception. Instead of recording the change of 30 classmates, record the average change of 30 groups of 5.

  1. 1. Randomly survey 30 groups of 5 classmates. Record the values of the average of their change.
    Table 3
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
  2. 2. Construct a histogram. Scale the axes using the same scaling you did for the section titled "Collect the Data". Sketch the graph using a ruler and a pencil.
    Figure 3
    Blank graph with frequency on the vertical axis and value of the change on the horizontal axis.
  3. 3. Calculate the following (n=5n=5; surveying five people at a time):
    • a. x¯ x =
    • b. ss =
  4. 4. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Discussion Questions

  1. As nn size 12{n} {} changed, why did the shape of the distribution of the data change? Use 1 – 2 complete sentences to explain what happened.
  2. In the section titled "Collect the Data", what was the approximate distribution of the data? XX ~
  3. In the section titled "Collecting Averages of Groups of Five", what was the approximate distribution of the averages? X¯ X ~
  4. In 1 – 2 complete sentences, explain any differences in your answers to the previous two questions.

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