Introduction to Science - Penny Histograms
This activity has benefited from input from faculty educators beyond the author through a review and suggestion process.
This review took place as a part of a faculty professional development workshop where groups of faculty reviewed each others' activities and offered feedback and ideas for improvements. To learn more about the process On the Cutting Edge uses for activity review, see http://serc.carleton.edu/NAGTWorkshops/review.html.
This page first made public: Aug 8, 2014
Results: The students find that 2 sets of pennies have overlapping weights (mean = 2.5 g, stdev = 0.2 g), while the third set is slightly different (mean 3.1 g, stdev = 0.2 g). The instructor can then lead a discussion around the topic of variability and how to statistically evaluate whether or not different data sets are statistically similar. This discussion should include how to account for instrumental error. This leads into a discussion of the meaning of mean values and standard deviation. This discussion can also include a comparison of how the results from an individual group compares with the data set from the whole class: this serves as a good place to discuss how scientists determine how much data to collect for a given project. This and similar exercises are thus needed before students start to interpret their own data. Expected Outcomes: Students will gain an understanding of how to read a histogram and how to evaluate the meaning of mean values and standard deviations.
Skills and concepts that students must have mastered
How the activity is situated in the course
Content/concepts goals for this activity
Higher order thinking skills goals for this activity
Other skills goals for this activity
Description and Teaching Materials
and for each group of students:
2 sets of 20 "new" pennies pennies with composition = 97.5% zinc, 2.5% copper (core: 99.2% zinc, 0.8% copper; plating: pure copper) = 1983 and later. The average weight of these "new" coins is 2.5g
1 set of pennies with "old" composition of brass (95% copper, 5% zinc) = 1962-1981. The average weight of these "old" coins is 3.11g
Note: coins from 1982 may have both compositions - a scape across the side or weights will reveal whether or not a coin has a zinc core
Penny Histograms (Acrobat (PDF) 197kB Aug8 14)
Teaching Notes and Tips
They often have particular trouble with choosing a bin size for histograms - I encourage them to start in pencil, and warn them that they may need to take several tries before they get a graph that is useful. I will give hints, but not the answers. This is where working in groups can be an advantage as different members of the same group can experiment with different bin sizes and they can compare answers to choose the best bin size for their group report.
Student are often intimidated by having to read and interpret graphs.
Submission of histograms and completed assignment by all students
References and Resources
Introduction to histograms: http://quarknet.fnal.gov/toolkits/ati/histograms.html
Histograms versus other types of plots: http://education.mit.edu/starlogo/graphing/graphing.html
An example of histograms: http://quarknet.fnal.gov/run2/histo.shtml
Selecting Bin size - adynamic histogram: http://quarknet.fnal.gov/run2/brian.html
Math is Fun: http://www.mathsisfun.com/data/histograms.html