I have been sorting and rolling coins for the past hour. This was just a pile of coins collected through the past few months. There are more quarters than anything else, then pennies, then nickels, and dimes are the scarcest.
Would there be an expected ratio of pennies to nickels to dimes to quarters received as change from day-to-day transactions?
The pile of coins I brought back after two weeks in the US agrees with your observation. Quite a lot more quarters than anything else.
On the assumption that:
(1) You only pay using dollar bills or larger; and
(2) The last two digits of prices that you pay are evenly distributed from .00 to .99; and
(3) The person giving the change uses the minimum number of coins; and
(4) You never selectively discard coins –
then you would expect the following ratios:
1.5 quarters
0.8 dimes
0.4 nickels
2 cents
since that’s the average number of coins you get in change each time.
If there are more quarters than cents, that suggests that prices are more likely to end in 0 or 5 than in the other digits, which violates assumption (2). (Another explanation would be that cents are lost more frequently than quarters, but that violates assumption (4) above.)
I would imagine the distribution of your pile of coins is roughly equal to that minted by the U.S. Treasury, adjusted slightly to your spending habits. Just a guess.
That’s a lot of work that I used to do, too. Then I discovered my bank will take a bucket of coins as a deposit and handle the sorting for free. Does yours do that?
Alternatively there are some public coin sorting machines in stores like Wal-Mart, but they charge about 10% of the total value.
In both cases, they give you back the paper clips, buttons, stones, rubber bands and trinkets mixed in. You know – the ones you thought you had lost.
Slight hijack, but Coinstar has a promotion right now where if you change in $40+ and opt for one of their gift cards you get a bonus $10 gift card. Check out their website to find the closest machine and see which gift cards you can get. I got one for iTunes, and I think there is Amazon as well.
Most items cost $x.99. Does that matter at all?
Yes, that would affect the distribution. However, you need to factor in that people may buy more than one item in one transaction, and that in the majority of transactions sales tax is added. But, even so, if everything has a price ending in .99, then the distribution will be uneven.
Thanks both for the math info and the Coinstar info. I knew they charged a fee so I didn’t pursue them. Too bad I missed the Amazon bonus.
Giles, I think your distribution is off, because it assumes that people only receive coins. But they will also spend them in some cases, which will likely skew the distribution, because I would think that the larger denomination coins will tend to be used more than the smaller ones - pennies in particular just end up in your pockets.
When I roll coins once a month, my distribution roughly matches jsgoddess’, but with dimes and nickels reversed - i always have more dimes than nickels, which comes closer to Giles’ proposed distribution. (And of course, I have more $1 and $2 coins than she mentions. 
)
I agree – selectively spending some coins rather than others does change the end result.
If you are the type who always takes change and never gives change, the answer is yes and I don’t know the percentages. In the same way that letters of the alphabet are used in certain percentages, change runs the same way. Anything you do that is unusual will change the ratio. If you are always getting gum with a dollar and taking 14¢ change, your ratio will be different. The fact that you went a long period before checking would offer the opportunity to check your ratio and compare it down the line.
I don’t like to give change and slow the checkout line down even a second. And I also resent giving 9%+ to the CoinStar machines. I have adopted a plan where I spend the quarters on vending machines and plug the coins into the slot at the self-service cashier stores. Now I’m not building up extra coins. That’s my plan.