Average Number of Hours Students Report Studying Weekly
Synopsis: An activity illustrating variability among sample means.
Students form groups of size four, write down the number of hours they
usually each study per week, and calculate the average. Then, the
means are written down in large figures on sheets of paper and shown to
all other students in the class. Finally, groups are combined to
illustrate how variability decreases with sample size.
Type of activity: In-class, small group
Statistical topics: sampling distribution of means, variability
of means
Time needed: 15 minutes
Materials needed:
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An activity form (Word97 Version, PDF
Version) for each group
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One large pen or marker for each group of 4 students
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One large sheet of cardboard or white paper for each group of 4 students
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An assistant to distribute and collect materials, and to enter responses
into computer file for analysis
Procedure:
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Ask students to break up into groups of exactly 4 students. Ask that
each group designate one student to be the "first reporter."
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Give one activity form, one marker, and one large sheet of paper to each
group. Ask the students to complete the form.
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Students should calculate their group's average number of weekly study
hours. Then, the reporter should write the average as large as possible
on one side of the sheet of paper or cardboard that was provided.
(The reporter should also write the word "four" in the bottom right corner
on the sheet.)
-
When all of the groups are ready, ask all of the reporters to raise their
sheets high, at the count of three, to show their average to the rest of
the class.
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The instructor should analyze the results with the students, including
determining the minimum, the maximum, and the range (as a measure of variability).
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Ask the reporters in adjacent groups to compute the average of their two
groups (the average of two means being the average for the group of eight
students). The two reporters should agree on who will be the "second
reporter." Then, the second reporter should write the result on the
other side of the paper. (The second reporter should also write the
word "eight" in the bottom right corner on the sheet.)
-
When all of the groups are ready, ask all of the second reporters to raise
their sheets high, at the count of three, to show the average for eight
students to the rest of the class.
-
The instructor should analyze the results with the students, including
determining the minimum, the maximum, and the range (as a measure of variability).
-
The assistant should then collect the large sheets with the reported group
means, and enter them into a computer file. Once the data are in
the computer file, the instructor can discuss the distribution of the sample
means by displaying a histogram and numerical summaries of the group means.
Comments from others who have tried activity: None.
Supplementary materials: Activity Form: Word97
Version. PDF Version.
This activity was submitted by William L. Harkness: wlh@stat.psu.edu