I have a one gallon pickle jar sitting on my desk. Right now, it’s exactly half-full from all the loose change I’ve collected over the years.
Is there any way to estimate how much money I’ve gathered? Assume that I have roughly equal numbers of pennies, nickels, dimes, and quarters.
First off, there wouldn’t be an equal number of each coin. You’ll have more pennies, then quarters, then nickels, then dimes. You might just weigh the jar (it’ll be damn heavy), subtracting the weight of a similar jar, then grab a few handfuls of the coins and weighing them. If you can’t get your hand into the jar, just spill some out instead. When you count those handfuls, it’s easy to figure the value of the entire jar by dividing the weights and multiplying by the smaller value.
How do you figure that?
Its because of mintages and change. More pennies and quarters are minted an other coins, and for all change of .01 to .99, you will usually get max 4 pennies, max 3 quarters, max 2 dimes, and max 1 nickle.
How accurate do you want to get? I was able to get an extremely accurate estimate by separating 20kg of coins into pennies, nickels, dimes and quarters and then weighing each group on a x.x gram scale. I got within a dollar. But, i also separated all the copper pennies 3.1 gram) from the zincs (2.5 grams.)
Another method: Maybe you can ask a hundred people (starts at 1:30)? In that experiment, 116 people were asked to estimate the number of jellybeans in a big jar. Their replies ranged from 400 to 30,000, but the final average was within 0.1% of the actual answer…
If we assume that every purchase you make has a random number of cents, that you always pay with a whole number of dollars and get change, that the change was made with the minimum number of coins, and that all coins you get go into the jar indiscriminately, then your coins will be in the ratio 15 quarters : 8 dimes : 4 nickels : 20 pennies. If you got every possible amount of change, the totals would be 150 quarters, 80 dimes, 40 nickels, and 200 pennies.
In practice, these numbers will be off, with the reality most likely favoring dimes and nickels more than those numbers suggest, for a few reasons. One, you’re not always going to pay with a whole number of dollars: If something costs $20.01, for instance, you’re probably going to find a penny somewhere (maybe from a leave-a-penny dish) rather than getting 99 cents in change. This will tend to lower the number of pennies. Two, some coins might not ever make it to the jar: If the change is just a few cents, you might just drop them rather than carrying them home at all. This will again tend to lower the number of pennies. Three, you might specifically look for quarters to use for other purposes, such as coin-operated laundry machines, which will tend to lower the number of quarters.
I would guess around $150-$200. I’ve seen these “guess the change in a jar” things come up before on Facebook and on the internet, and, typically, they end up about $300-$400 per gallon for random pocket change. YMMV. No formula, just reporting the results I’ve seen. If it’s truly an equal distribution, I would guess at the higher end of the range.
I would just roll up the damn things.
I just counted my coin jar, there were more $2 coins than any of the lower denominations. $1582 weighed 16.2 kg (or 18.2)
Tell me the logic of the ratio…
Every denomination mod-25¢ coin?
ETA: Can I use this information to get into MIT and get power?
What’s a $2 coin?
Basically, I made a huge table with the coins used to make change for 1 cent, for 2 cents, for 3 cents, etc., up to 99 cents, and then (since I was assuming all of those come up equally often) I just totaled them.
Top right (the non-furry top right, that is)
The best I can tell you is, back in happier financial times, I used to also toss all my change into a coffee can. After a few years I had accumulated about three or four of them, each full to the top with coins. At some point I needed extra money so I would periodically take them to a Coinstar machine to cash them in. Every time it wound up being around $350 (more than I initially expected!)
I don’t know exactly how a coffee can converts to a gallon. They contain 39oz of coffee, but that’s weight not volume. They look roughly similar in size, a coffee can probably holds a little less than a gallon.
I know a lot of people bemoan the fact that **Coinstar **machines charge a percentage fee (last time I used one it was 9%) to count your coins, like it’s a ripoff or something. But I can’t think of a more aggravating, time-consuming, tedious process than sorting, rolling & wrapping freakin’ coins! Not to mention the fact that it would probably take all day to do a coffee can’s worth. Plus you have to take them to ***your ***bank (if you don’t have an account banks won’t accept large quantities of coins, even rolled) to cash them in. Coinstars are a godsend as far as I’m concerned…
I thought you had an analytical (mathematical) method. (I always think of Chronos and his cohort here as ratiocinating the fuck out of everything from some single thought, leaving simple counting for mortals.)
There must be a math expression governing the result/problem. Right? Right??!
ETA: to Chronos
You don’t have to roll your coins to take them to a bank; banks have coin counting machines. Maybe not at every small branch, but I’ve never lived anywhere where there wasn’t at least one branch in town that would take your coins, dump 'em in a machine, and deposit them in your account/give you cash.
Yeah, you probably have to have an account at the bank, but even now, in the days of digital everything, I typically have to go to my bank physically at least a couple times a year to do something or other. I just bring my coins in at the same time. Never has been a hassle, or a charge, or have they been anything but happy to do it.
A quart of pennies is right around $13 (if you can trust a Coinstar machine).
Fresh beans:
0.52063621494641
Roasted beans:
0.67610397357624
according to Weight to Volume / Volume to Weight Converter
(one of my favorite sites)
Yeah, I could (and should) have done it smarter than just a big table. But I’m tired, and didn’t feel like thinking too hard, and the mechanical brute force method doesn’t require much thought and works fine.
Well, be sure to get some rest. Oh, and by the way, it would be best if you have it on my desk by, I don’t know, noon tomorrow, ok?