ID Information: LastName, FirstName, date, Locker #, Course/Section #, lab partner’s name
The purpose of the experiment was to determine experimentally the variations in the mass of pennies both within a single mint year and over a range of years. The expected outcome is that the variations determined in the mass of the pennies both within a single mint year and over a range of years will be minimal.
References:
Suzanne Slayden, 2015, Chemistry 211, 212, 251 Laboratory Experiments, 6th Edition, GMU Bookstore, Johnson Center, page 7 - 9
Materials and Chemicals:
The materials required for the experiment are:
An electronic balance
Pennies from a range of mint years.
Procedure:
The procedure of the experiment is as follows: (Suzanne, 2015)
Pennies from one mint year were selected from the pennies provided for the experiment
Using a single balance the precise mass (in grams) of each of the pennies selected from specific mint years was determined and noted
The data collected from the mass measurements was then recorded in the laboratory notebook after the mass of each penny was determined
A precision of 0.001 g was used in recording the mass determined
The procedure was repeated for 10 pennies for each year
Once one mint year was completed pennies from another mint year were selected and the procedure repeated from 1986 to 1994.
Ms. Excel was used to organize all the data collected in tables and the average and standard deviation from each year was determined.
Data:
Using Ms. Excel, the data collected from the experiment was organized as shown in table 1 above. The table below includes all the raw data collected (penny mass measurements) from the experiment. It includes the ten mass measurements made for each mint year, as well as, the averages and standard deviations calculated of each individual year.
Observations:
During and after the experiment it was observed that the variations determined in the mass of the pennies both within a single mint year and over a range of years were minimal.
Results and Calculations:
Using Excel, the scatter plot shown below was plotted. The scatter plot shows the average mass vs. year on the primary y-axis and standard deviation vs. mint year on the secondary y-axis.
Chart 1: Average mass vs. mint year for coins
The results of the experiment are shown in table 1 above. Each row in the table shows the 10 mass measurements of pennies from a particular mint year. For the calculations, the AVERAGE () and STDEV () functions were used to calculate the average and standard deviation of the mass of the pennies measured during the experiment. In addition, the standard deviation for all pennies was also determined. These figures are included in table 1 above.
Sample average calculation for 1986:
Average = (m1 + m2 + m3..+ mn) / n
In this case, n = 10, therefore,
Average = (m1 + m2 + m3..+ m10) / 10
For 1986,
Average = (2.54 + 2.515 + 2.535 + 2.519 + 2.482 + 2.547 + 2.488 + 2.528 + 2.490 + 2.520) /10 = 2.516
Discussion and Conclusions:
Based on chart 1 above, the trend observed in the variation of average mass with mint year ranges from a minimum of 2.5 g to a maximum of 3.1 g over the years that the mass of pennies was measured during in the experiment.
Examining chart 1 above, minimal variation in standard deviation with mint year is the trend observed other than on 1988, which has the highest standard deviation (as observed in the spike present in the chart above).
The possible explanation for the variation in average mass with mint year ranging from a minimum of 2.500 g to a maximum of 3.100 g over the years is that government regulation requires pennies to have a mass of between 2.500 g and 3.100 g. This implies that the penny minter has a specific tolerance range within which they can mint pennies. In this case, the noted tolerance range is ± 0.600 g. The most possible explanation for the minimal variation of standard deviation over the years is that the mass of the pennies each year does not significantly vary from the average mass from the same year. However, in 1988, it is evident that some of the mass measurements taken greatly vary from the mean, hence, the spike seen in the chart.
Another possible explanation for the variations noted in the mass of pennies especially, the spike noted in 1988 is the change of minting equipment. New equipment used by the penny minter may have different a different tolerance range, hence, leading to pennies with a greater variation in mass. Lastly, there is a possibility that the minter improperly and erroneously minted the penny from 1988 with a measured mass of 8.522 g since this is an outlier value as compared to all the values collected from the laboratory. This in turn led to a high measured mass value, increasing the average for the year, and, leading to the highest standard deviation for the year.
In conclusion, the objectives of the experiment were achieved. Additionally, with the exception of one outlier noted in 1988 the expected outcomes were observed.
