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Statistics Question: How Old is this Bar?
What you’re looking at is a bar made by arranging roughly a hundred bucks* in pennies over the surface and coating them in plastic. I can read the dates off of some of the pennies (those that aren’t flipped upside down), but quite obviously not all the pennies were minted in the same year.
Here’s the question: Judging solely by the dates these pennies were minted what year was this bar constructed? How many dates would I** need to read to have a reasonable confidence in that answer? Should I bother taking dates off of the dull pennies, or only focus on the shiny new ones?
*I arrive at this number by a Fermi estimation. Assuming the bar is twenty feet long, two feet across, and that the radius of a penny is 9.775 mm (thanks Bing) how much is it worth?
**Well, not me personally but I do have a research team nearby. I doubt I’m welcome back in that establishment after telling the bartender that she was going to have trouble finding her tip.
Published in Science & Technology
“Filthy Casual” :-)
Confidence in the answer decreases as the most recent dated coin is further from the current year.
If you find a coin dated in the current, you can say with 100% certainty the bar was built in the current year.
If the most recent coin found is 10/20/30 years old, confidence that the bar was built in that year and not more recently is lower. Why?
My pennies:
Text available on request.
This looks odd, but is largely consistent with expectations of an exponential drop-off. However, this is my snapshot counted in 2023, and it is clearly not representative of coins in circulation, what with absolutely none from the past two years. (I effectively no longer use coins or money except in rare cases).
It’s informative, but hardly definitive. I haven’t added to it recently — that’s for sure.
It is not so odd as it looks, however, when you take the following mint data into account. This also addresses @doctorrobert‘s concern about missing money:
We should each expect to find a dearth of pennies from the early 2000’s to maybe five, seven years ago. Suspected recency bias certainly is represented in examples posted so far, so even if 2021 and 2022 maintained the 2015-2020 average, we should expect to see plenty of those recent ones.
The island of 70s through 90s pennies in our collections is due to massive production in that period, and bordered by expected scarcity in the past, and unexpected lack of production more recently.
I applied an exponential decay set at 2.5% loss per year (orange line). This is selected utterly arbitrarily.
We’re closing in on a reasonable expected distribution of pennies under the bar.
Are you asking the question that the quoted matter here just addressed?
There are two broad ways to address this whole thing. One is to begin by collecting facts and constructing a model which does not exceed those facts. This is likely to yield premature optimization, and a model fit to answer only a specific instance of a question, e.g., this bar. The other is to construct a model from principles and then fill in variables with facts discovered. This is likely to yield a model fit to answer any such question, including the one at hand.
I confess to the second. That is why I am (for now) ignoring some specifics.
I take a Seinfeldian pleasure in spending my last coin. Doesn’t happen much.
I kept checking his diagram when he mentioned flukes to see where they fell on the graph.
The pennies were placed by hand. They might have been placed face up by some just because. And some people may have grouped pennies by date or darkness on a whim. Or some might have deliberately scattered the bright ones throughout the bar for symmetry and bright accents.
If I were doing it, I would have laid the various colors to show a large image of a penny in the center of the counter — with Lincoln’s head facing to the left. Otherwise, laying out pennies is quite boring.
It was wrong to put your two cents in. Invalidates everything.
Kinky.
People who have unlimited time and money to find the answers to questions can afford to be averse to using statistical methods. It can sometimes be useful to know which people around you have unlimited time and money.
Kinkier!
Mind, I don’t mean to be uncharitable. I’m just hollering statistics.
Kinkiest?
Yeah, that’s a lot more variation than I expected even considering your comment some ways up thread. I was thinking you might be able to normalize the numbers for the purposes of curve fitting but when you’ve got seven times more pennies minted in 2000 than 2008 I’m not sure I’m comfortable with that much adjustment.
I’m not so much interested in the solution to the problem as how I’d go about finding it. Because the next question might not be about a bar top, and there might not be an owner to ask.
That’s a fine looking bar you’ve got there. I’d look even more fine with a cold pint on it. Just sayin’.
The way I’d go about it, I’d take a handful of pennies and plop ’em down on the surface, then push ’em around with my hand until they’re all flat. That would be easiest for me, but would give you the single layer of random facing, rotation, shininess and date that you’re seeing in the photo. (Probably not the dates. I spent some time looking at the original photo and I think I can just barely make out the numbers 2014 on the shiny guy in the second row, but I’m not confident in that and anyway one data point isn’t a proper sample.)
Uh, back to what I was saying your method would make a much cooler bar. With all that horizontal room though I might take another set of pennies, blacken them deliberately, and then make John Wilkes Booth aiming at him.
A bistro with a Lincoln bar and a John Wilkes booth? That’s a good start.
That’s a good idea. Or pointing at Mount Rushmore.
I would think that there could be great subtlety in a mountain scape done with aged pennies. The shiny ones could help the sun and the clouds, and the sparkle of the mountain streams.
But, um, isn’t artificially blackening the pennies sort of inorganic, artistically speaking? I’ll have to consult my text on that, The Art of Lacquer and Loose Change by Penny Pixel.
But who pays for lunch?
That confederate scrip is no good around here.
Blackening any face will, if you are a Republican, get you cancelled. Wearing blackface will not, if you are a Democrat, prevent you from getting elected.
Hypothetically, if I’m already black, and a Republican, will wearing a normal face get me cancelled? I think it actually will.
Going to put up a separate post for gathering penny distributions from folks.
Drop a link when you do.
Capital idea!
https://ricochet.com/1370562/post-your-penny-counts-by-year/
July 31st, 2023, in the Westby Cooperative Creamery, Westby, Wisconsin.
Well. More than half a year then; round up a good bit and I’m half right. But it does throw off my calculations. Now where is that envelope.
My hunch is that we’d discover the new coins earlier if we were doing more cash purchases.
I do cash purchases but I don’t even count my change. I don’t even pick up pennies off the sidewalk anymore. Isn’t that decadent?