Common cents
Please read the general guidelines first!
Objective
To investigate how long coins remain in circulation.Materials
- At least $20 worth of 5 cent pieces.
- Pen and paper for recording data.
- Australian coin collectors guide (perhaps from the library)
Methods
- Check a coin collectors' manual for the number of 5 cent coins minted each year since 1966.
- Record these production numbers and note the last year for which the information is available.
- Place all of your 5 cent pieces in a pile and go through them one-by one, recording the age of each on a tally sheet. (Exclude any coins which were minted after the last year for which you have production figures.)
- You should end up with two numbers per year: (i) the number of coins minted; and (ii) the number of coins in your sample.
Analysis
- Construct a two-way table with Number minted and Number in sample across the top, and year down the side.
- Record the counts of number of coins in the sample and number of coins minted.
Here is an example (where the figures are obviously made-up):
Year Number minted Number in sample 1966 3000 150 1967 1000 0 1968 2000 200 1969 5000 1000 1970 4000 200 Totals 15000 1550 - Calculate the column percentages for the two-way table. That is, the percent of the sample minted in 1966, 1967, 1968, etc in the first column, and the percent of the population minted in 1966, 1967, 1968, etc in the second column.
- Subtract the percentages in the sample column from the corresponding numbers in the population column.
This will give a column of difference scores, one for each year.
Continuing the above example,
we would get:
Year Number minted Number in sample Difference 1966 20.0% 9.7% 10.3% 1967 6.67% 0% 6.67% 1968 13.3% 12.9% 0.4% 1969 33.3% 64.5% -31.2% 1970 26.7% 12.9% 13.8% Totals 100% 100% - Some of the differences will be negative and some will be positive.
- You may choose to present the differences as a bar chart.
The bars corresponding to negative values will hang down below the x-axis;
those corresponding to positive values will push up above the x-axis.
Discussion
- Identify any missing data (eg date illegible) or other problems in your data collection (eg lost count).
- If large numbers of coins have been taken out of circulation (worn out):
- The longer since the coins have been minted, the more of them which would have been taken out of circulation. Earlier coins should be under-represented in the sample and earlier years should have more negative difference scores.
- If relatively few coins have been taken out of circulation:
- We would expect the differences between our sample results and the population results to be just random variation (because the sample provides an incomplete count of the entire population of coins).
- The characteristics of random variation is that about half of the differences would be negative and about half would be positive, and the negative results will be spread reasonably evenly across all years (not clustered into the earlier years).
- Explain that the sample is likely to differ from the whole population of coins currently in circulation because the sample contains less information. Explain that part of the differences between the sample and the population is caused by taking a sample.
- Determine whether your results suggest that earlier coins have been taken out of circulation.
- Estimate how long coins last before they start being taken out of circulation in large numbers.
- Suggest any improvements which you would make if you were running the study again.