The Average Value of a Coin
For reasons that are too stupid to write down, I decided to try and figure out what the average US coin is. I love a good stupid statistical adventure, especially when I should be sleeping instead of working on a spreadsheet.
First, let me shoot down the easiest approach. We could just take the average of 1, 5, 10, and 25 cents. If we did this we’d get 10.25¢, but there’s a factor I find more interesting: the actual number of each coin that gets produced. In other words, I want an average that’s weighted by the number of coins produced.
To do this, I need some source on how many coins actually get minted each year. Luckily, Wikipedia swoops in with a table showing coin production since the year 1887! (https://en.wikipedia.org/wiki/United_States_Mint_coin_production)
Copy+pasting this into Google Sheets, I was really surprised that it automatically formatted everything correctly--I was worried the whole table would get pasted into a single cell, which would be stupid. This made my job with data cleaning very easy--I just had to delete citations to make everything recognized as a number. absolute best they’re gonna get is actual pants At this point, I also decided that I wanted to find the average mass of a coin so I quicky searched around for how much coins weighed. I also decided to limit my date range to 1982 and later, because the mass of a penny varied way more before that time.
| Coin | Value ($) | Mass (g) |
|---|---|---|
| Penny | 0.01 | 3.111 |
| Nickel | 0.05 | 5 |
| Dime | 0.10 | ~2.2 |
| Quarter | 0.25 | ~5.7 |
NOTE: The Wikipedia table also tracks half dollars and dollar coins, but I’m choosing to ignore these because I don’t really care about them.
With this, I can sum up the number of coins produced since 1982, and use that to derive the total value and total mass that have been minted.
| Coin | # Produced | Total Value ($) | Total Mass (g) |
|---|---|---|---|
| Penny | 3.87e+11 | 3.87e+09 | 1.20e+12 |
| Nickel | 5.23e+10 | 2.62e+09 | 2.62e+11 |
| Dime | 8.98e+10 | 8.98e+09 | 1.97e+11 |
| Quarter | 8.45e+10 | 2.11e+10 | 4.82e+11 |
Two main things to note from this table: - These are MASSIVE numbers! There have been 3.7 billion dollars of pennies produced alone. - The most-produced coin is pennies, by a whole order of magnitude. I didn’t expect this, I feel like I see higher denominations more often! Maybe I just don’t notice pennies.
At this point, I can actually answer my initial question by taking these averages:
sum(values)
average coin value = ------------- = $0.06
sum(number)
and
sum(masses)
average coin mass = ------------- = 3.5g
sum(number)
There we go, all done!
The average coin in the US since 1982 weighs 3.5 grams and is worth 6 cents--a slightly lighter and more valuable nickel.
This is interesting to me because it shows that the massive number of smaller denomination coins---particularly pennies---drags the average way towards the lower denomination data, both in terms of value and mass.
-
Since 1982, the weight of a penny has either been 3.11 grams (for copper-plated zinc coins) or 2.5 grams (for brass ones) according to https://cointrackers.com/blog/43/how-much-does-a-penny-weigh/. I’m sticking with the 3.11 gram measurement because I want to simplify some. ↩
