Chemistry Everyday for Everyone
An Easy and Effective Classroom Demonstration of Population Distributions Marjorie A. Jones* Department of Chemistry, Illinois State University, Normal, Il 61790-4160
While we as science teachers are comfortable with the concept of a normal (Gaussian) distribution of behaviors for atoms, molecules, organisms, or populations, this concept is often difficult for students. This may be especially true at the middle school, high school, and freshman college levels. The development of an easy, inexpensive, and effective classroom experiment to evaluate distributions was, therefore, the goal of this work. The experiment uses readily available material, is safe, and can be modified in many ways to expand the major concept. The experiment was performed during one 50-minute class period (in a class having 27 students), and a second class period was used to further discuss the data, their interpretation, and conclusions. The Experiment For a class of freshman nonscience majors, the following experiment was undertaken. Students worked in teams of 3 or 4. Each team was given the handout (see box) and graph paper and was asked to follow the instructions using the hot-air popcorn poppers and a measured amount (80– 90 grams or 600–800 kernels) of popcorn. Each team was given a different time interval for which to collect data. These times ranged from 5 seconds to 45 seconds. We used four popcorn poppers; therefore, the teams had to take turns. Since this goes fairly rapidly, each team required only about 6–8 minutes to collect their data. The popped corn was collected in soup bowls (each team was given three) and the students quickly learned to make piles of corn on the bench tops for each time interval. The teams were asked to work out an experimental strategy before starting the actual experiment. The teams who went first struggled a bit with their data collection, since *Email:
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No. of popped kernels
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they had not anticipated all the problems (which included popcorn scattering as it came out of the hot-air popper). Also, about midway through the popping, when the majority of kernels are popping, there is too much corn to catch in a single bowl. Students also struggled to decide how to count the broken or partial kernels. The teams that followed rapidly modified their experimental approach as they watched the first teams, so that they were more confident in their data collection techniques. This activity thus required the students to do a lot of decision making relative to their experimental design. After counting their popped and unpopped kernels, students plotted the number of collected popped kernels per time interval (as the dependent variable) versus time from adding corn to the popper (the independent variable). A representative graph is shown in Figure 1. The students were clearly able to see that the popcorn popped with a normal distribution and not all at once. The normal distribution is completely determined by two constants (parameters), which are the mean (µ) and the standard deviation ( σ) as discussed by Snedecor and Cochran (1). The mean and standard deviation for the time data in Figure 1 were 11.0 minutes and INSTRUCTIONS FOR EXPERIMENT GROUP NAME: GROUP MEMBERS___________________________________ DIRECTIONS FOR EXPERIMENT TO TEST THE POPULATION DISTRIBUTION OF POPPING CORN: 1. Preheat hot air popper for about 3 minutes. 2. Add measured amount of kernels. 3. Collect popped corn in a selected time interval. (TIME INTERVAL = _________ seconds) 4. Count the number of popped kernels for each time interval. 5. Count the number of unpopped kernels. 6. Plot the number of popped kernels for each interval on the “y-axis” versus the time on the “x-axis”. 7. Calculate the percent of unpopped kernels. 8. Draw a conclusion (or several) about your corn population distribution. 9. Speculate (by writing an argument) if your conclusion is a “universal truth” that can be applied to other populations.
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PERCENT OF UNPOPPED KERNELS ____________
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CONCLUSION(S):
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6 7 8 9 10 11 12 13 14 15 Time interval
SPECULATION:
Figure 1. A representative graph showing the population distribution of popped kernels across consecutive time intervals.
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Journal of Chemical Education • Vol. 76 No. 3 March 1999 • JChemEd.chem.wisc.edu
Chemistry Everyday for Everyone
± 2.7 minutes, respectively. About 66% of the observations lie in the interval of mean ± 1 σ and about 95% of them are in the interval mean ± 2 σ, which are classic characteristics of the normal distribution (1). The students also found that the time intervals at which they collected data influenced the type of population distribution pattern plotted. Most groups reported a fairly smooth population distribution. The average time for the peak interval was 9.1 ± 1.7 seconds. The clean-up for this experiment is fairly easy. It involves discarding the popcorn, wiping out the poppers, and sweeping the floor. Before and during the experiment, students were reminded not to eat the popcorn. There are no lab safety issues with the experiment, since the heating element of the popper is already inaccessible so burns are unlikely. During the next class period, we compared the data from the different groups and discussed the results. For the brand of popcorn we used, the percentage of unpopped corn was fairly consistent from group to group (1.1 ± 0.8%). We discussed the implications of distribution curves. We especially discussed why the distribution patterns were different (relatively broad peaks or relatively sharp ones) for different groups. and therefore could see an influence of sampling interval. We then extrapolated from the distributions of corn popped to molecular behavior in
chemical reactions. We discussed the concept that not all of the reactants undergo a chemical reaction at the same time; there is a distribution of times, and this is related to a distribution of associated kinetic energies of the molecules. We also discussed the implications of the popcorn experiment for other fields of science, such as the development of pharmaceuticals, drug testing, biomedical research, and social science research. This was particularly of interest to the students, as we discussed the likelihood of all persons in a population responding exactly the same way to a drug. From this discussion, the students felt that not all persons would respond exactly the same way and that they should expect some variation. Other activities could involve comparing various brands of hot-air popcorn, correlating in terms of cost effectiveness the percent popped with the advertisements proclaiming who has the “best” popcorn. This, then, allows nonscience students to directly correlate their data with their real life. Literature Cited 1. Snedecor, G. W.; Cochran, W. G. Statistical Methods, 6th ed.; 1967. The Iowa University Press: Iowa City, 1967; pp 32–35.
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