Average value of coins returned in change per pound

So many discussions on the ending of the cent, many about rounding and how many cents are typically paid out per cash transaction. For grins and giggles, I did a calculation using the fewest coins back for each of the 99 possibilities. A few of the returns:

Average number back per transaction

1¢ - 2.02 5¢ - 0.40 10¢ - 0.81 25¢ - 1.52​

Average weight in ounces per transaction (used 2.8g for cent, average copper/zinc)

1¢ - .20 5¢ - .07 10¢ - .06 25¢ - .30 ​

Count of each to equal 1 total pound based on averages above (25.2 transactions)

1¢ - 50.9 5¢ - 10.2 10¢ - 20.4 25¢ - 38.2​

Dollar value per counts in line above

1¢ - $0.51 5¢ - $0.51 10¢ - $2.04 25¢ - 9.54
​

Hopefully I don't have a major blow, I enjoy math but sometimes it doesn't like me. I come up with $12.60 per pound.

I have mentioned in the CRH forum that I offer to "purchase" change from friends and family, at full value rounded up to the next dollar. Saves them from having to return to the bank or worse yet lose money in a Coin Star. My brother recently took me up on it and I got the bucket below from him, which as you can see weighs 28.4 pounds. I don't want to remove the coins yet, I don't like jostling them around more than necessary, so not exactly sure about the bucket, I'm going to estimate 10 ounces. That would leave about 27.8 pounds. Based on my calculations I will guess the value to be:

$358.28

Anybody else care to guess? Not sure how long it will take to separate and count but as soon as I do, I will post it.

 

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I have two identical piggy banks. I put quarters in one and the other denominations in the other. They both fill up at about the same rate. This information is useless for the purposes of your calculation.

Hard to judge your volume of coins but looks to be almost double my piggy banks, which typically have a bit over $200 in them. So I'd say your estimation is pretty close.

 

I like this - it's a nice twist on the usual conversions between value and weight based on coin type.

Based on my recent experience, I'd put the average weight per cent closer to 2.5 or 2.6g - I could go through several transactions without seeing copper cents, just before stores stopped giving them. Now, with the "penny drives", we may well start seeing more copper cents in change, though!

I've had self-checkouts return two nickels instead of a dime. That would really throw things off - 10g vs. 2.27g!

 

$342.50
I took a pound off for the container. (27.4lb)
I also figured $12.50 a pound for random change...$12.50 is easier for me to remember.
It helps to put the change in a plastic bag, Ziploc or shopping or trash bag.
The bag eliminates container weight.

 

I agree, should have adjusted the cent weight down due to higher percentage of the zincs. Any guess on the value?

I use ziplocs for smaller quantities, but otherwise I like something rigid so that the coins don't get jostled as much and cause additional "bag" markings.

I will weigh the bucket once it's emptied and post.

 

Just to note the trick my mind played on me when looking at the bucket in the pic: Along the left side inside the bucket is a lighter shade of yellow and to me that instantly looked like the bottom of the bucket, making the left side of the coin pile appear to be segregated rather impossibly. Anyway...

 

I sorted the change into 4 coffee cans and wanted to get the weight of the plastic bucket. The pound weight scale wasn't sensitive enough, and it overloaded the gram scale. We don't have an ounce scale, so I tried something else. I got two large plastic containers, the first was just a little bigger than the bucket and the second large enough to hold the first (see pics). I put the first one in the second then filled it to the brim with water. Then I took the bucket and gently set it on top of the water until it was floating with only a light touch of my finger keeping it balanced. Then I removed it and the first container from the second and dumped the displaced water into a measuring cup. It was right at 100 ml. A web conversion ap showed that to be about 3.5 ounces, or .22 pounds. The filled bucket was 28.4 so will take it to 28.2 pounds.

Should have the coin counts on Wednesday.

 

Wow that's one way to get the job done.
I probably would have stepped on the scale and then picked up the bucket...not very accurate to the gram/ounce but less production I like your way better.

 

We think alike @rte - I tried that, but the scale didn't change when I picked up the bucket, just not sensitive enough. We may find that the original weight was off, will know when we get the total count of all of the coins.

 

Average weight of a 1 gallon bucket...your in the Ballpark 248 grams =
0.547 pound

 

We’re going to round do does it really matter?

 

Not really, but it's fun to experiment.

 

Did the quarters late yesterday, count was 774, $193.50. In the photo the stacks are 20/$5 high.



May not get the rest done today, mom has a turkey-emergency I'm going to have to go over and help with. If not today, it will be Friday.

 

Dimes went fast, 865, $86.50; total so far $280.50.

The initial coin average per transaction is already blown, at least between quarters and dimes. I had a 15:8 (152/81) ratio estimate, and this round came out at 15:17 (774/865). There is the possibility that quarters were pulled out for carwashes, soda machines, etc., but so far, my prediction is way off.

 

Hmm, is something wrong with your math or logic? It seems odd that your calculation says that on average you would get back almost twice as many quarters as dimes. My brain doesn't work as well as it used to. But for every .25 multiple of change back, you could get 0, 1, or 2 dimes back. 0.00-0.24 you get 0 quarters back and 0, 1 or 2 dimes, 0.25-0.49 you get 1 quarter and 0, 1 or 2 dimes, 0.50-0.74 you get 2 quarters and 0, 1 or 2 dimes, 0.75-0.99 you get 3 quarters and 0, 1 or 2 dimes. So below 0.50 in change, two-thirds of the time you'll get either 1 or 2 dimes back and half the time either 0 or 1 quarter. It seems like the odds are good that you get as many or more dimes back than quarters. Above .50 you are guaranteed to get as many or more quarters back than dimes. But does the actual overall probability match your original 15:8 quarters to dimes ratio? My brain hurts.

 

Your logic is good, but the major difference is that once you are over 75¢ you are guaranteed to get 3 quarters. That's 25% of all transactions. Since you will never get 3 dimes the ratio moves hard towards quarters when you get to the higher value returns.

 

Here's the nickels - 506, $25.30. Up to $308.30. No way we will get to my estimate of $358.28 with just the cents left, mainly due to the lower volume of quarters than predicted. The dime to nickel ratio is fairly close, predicted right at 2:1 in favor of dimes, came in at 1.71:1

 

Understood, and this is where I struggle. On the low end, 66% of 25% of the transactions you get more dimes than quarters (one or two dimes and 0 quarters). On the surface it just seems like it would be closer to even, instead of almost 2:1.

 

I’m running into some people in stores that are furious over rounding.

 

Wow. I haven't yet found a store that ever rounds in their own favor; it's always to the favor of the customer.

In fact, I could probably turn cent into nickels. If my total was $10.00, and I put in a cent and then a ten-spot, I'm pretty sure the machines would give me back a nickel. No, I'm not going to try it.