I would give up on trying to find the "actual" numbers left in circulation--the dynamics of circulation, hoarding, and coin durability are far too fickle to calculate with any reasonable accuracy. Especially at a level appropriate for sixth grade statistical analysis.
What I would focus on is the concept of "half-life" and how it relates to other things--in this case, coins left in circulation. For the sake of the project, forget that rare and old coins are typically preserved better than common ones. Have your student do some research on "average coin life" in circulation to get an idea of how long a given denomination can survive the task of being used before it is too worn out and must be retired. For example, the number used to justify all of the various $1 coin programs is that a $1 coin will last 25 years in circulation compared to a paper dollar's 2 year average.
From there:
(At the risk of doing the work for you)
1. Gather mintage information for each year from the Internet (Wikipedia has comprehensive lists of most denominations)
2. Calculate each year's mintage as a percentage of the total denomination mintage (this can be done easily through Excel once your data are entered)
3. Using each coin's half-life in circulation, determine how many coins are "retired" each year (say a coin minted in 2004 has a half life of 10 years and a mintage of 1,000,000,000. In 2014, we would expect 500,000,000 to be freely circulating with 5% of the remaining population being retired each year)
4. Determine estimated total remaining population in circulation
5. Calculate probability of receiving a specific coin from circulation
And as a bonus:
6. Have your student check their data against actual numbers; e.g. estimate how many 2003 cents are left in circulation, and have them pull all 2003 cents from a $25 box of cents to check their estimate.
7. Have your student put together a collection of coins in varying conditions to show how coins deteriorate over time. Ask them to think critically about why condition and age may not always correlate.
8. Have your student extrapolate their data to estimate when the surviving population of a particular year will be equal to 1. Ask them to think critically about why their data will never show "0". (At the risk of teaching an 11-12 year old about limits
)
9. Have your student research the relation between mintage, condition, and rarity in "classic" series such as Morgan and
Peace dollars. Note that price and rarity correlate only weakly within these series. Challenge your student to discover why. (Answer: Many of these coins sat unused in government vaults until the 1950s while others circulated heavily. For example, an uncirculated 1885-O Morgan may be worth $30, while an 1892-O may be worth $200, despite being in the same condition and having a reasonably similar mintage.) Ask how perceived rarity might affect a coin's surviving population in the future (the 1950-D nickel is a prime example--just over 2,000,000 were made, but the public was aware of this and consequentially almost the entire population was pulled from circulation and survives to this day).
Hope that gives you some good ideas! Obviously, what is outlined above would be quite a task for a 6th grader. I would personally advise that you focus on one denomination (Cents 1959-2014 or Nickels 1938-2014 would be my recommendation) and would strongly recommend challenging your student to complete 6) above as a way to reinforce how to test hypotheses with real-life data. It may seem like a lot of money, but remember that you can always bring them back to the bank for a 100% refund!
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Posted 09/29/2014 1:15 pm
