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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
How do you know that barmaid’s gonna tell you the truth?
Are we still talking about fruit?
Thanks. This leads into my question about the shininess of the pennies. If I ignore any dull pennies could I get a better answer with a smaller sample size?
Ten thousand pennies is a lot to look at. Trust me, I’ve tried. And by the time you work your way to the end of the bar how confident are you that you’ve got a duplicate date, or were you just seeing double?
Because I’m interested in how the question is answered, not the actual answer.
Sorry, that’s not funny enough; let me try again.
Because the bartender had a tremendous pair of knockers and I was intimidated.
If it was easy all of those statisticians would find no takers.
The only Penny I ever dated was too bright to say ‘yes’ a second time.
I tend to think that the dullness is not particularly representative of age. And after writing this I pulled the change out of my pocket and there were four pennies. In order of darkness, one was quite dark brown (1995) — one medium-dark brown (1998) — one light brown (1964) — and one shiny copper (2017).
The two lightest ones were 50 years apart.
Different compositions of metal. In 1964 they were pure copper. Not sure when that changed.
Sure, but then you’re just doing two sequential samples.
All you have to do is keep the latest year seen so far in mind.
I think it was ’82 was the last 95% copper penny, and starting in ’83 they were zinc and I believe copper plated. But if darkness over time is a matter of alloy, this removes the statistical brightness-equals-newer scale, and you’d have to know the dates to know which scale to use, which means you’d still have to check the dates in the first place.
Probably looking only for shiny copper coins would cut the whole process of checking dates down by, from the glare it looks like at a glance, a good 60%.
Just check the shiny ones. Maybe sample four or five spaced and staggered square feet. And add two years because it takes a year or two to get into sufficient circulation.
Does it though?
New Year’s resolution: Announce the date I find the first 2023 penny.
I think so, fairly generally. I don’t really look at coins but I rarely see them in the first year of production, and fairly rarely in the second year of production. But how close are you determined to be in finding the age of the counter top. Even if you check the date of every penny, it still may not have the most recent year. And if you rely on sampling I would think it less likely to even have the second most recent year.
When you find your first 2023 penny, write a post about it to either correct or confirm this post’s final answer. :)
“You will never find the correct, absolute, and final answer. There is another question to follow your answer.” – Professor Kingsfield
I know when I found my first 1954 nickel, but I’m not sure if the year was 1954. I could figure it out, though, with the help of my mother’s diaries. It was when I was staying with my grandfather at his country store for a few days.
Well, they could always ask the manager. Why would he lie?
Alright, Karen.
Excuse me?
Karen always wants to talk to the manager.
I pulled the frozen mass of change out of the tray in my car. I cleared it out this fall, so any pennies in it were in circulation as of three months ago. Sorting by date I’ve got
4 from 2022
4 from 2021
2 from 2019
9 from earlier in the 2000’s, none later than 2016
12 from 19XX
1 Canadian infiltrator penny.
Taking the most recent penny found and adding two years for a safe estimate I can confidently conclude these coins were gathered no later than 2024, and I’m 95% confident that I’m an American.
Oh. I guess so.
All the shiny ones are in the 2000 or later category and all the dull ones are in the 1999 and before category. There’s variation (I’d rank the 2001 penny as shinier than one of the 2021 pennies) but the shiniest ones are all 2022.
Oops.
And you’re looking at the pennies??
I was a grad student in statistics once upon a time, but it was a very long time ago. I’m not sure which probability distribution would apply to this particular problem.
Answering would depend on what you mean by “reasonable confidence in that answer.” I don’t think that you can ever have very much confidence, because we don’t know the circumstances of collection of the pennies. For example, they could have been taken from someone’s old penny jar, and might not have included any pennies that were recent at the time that the bar was made.
BDB’s idea in #23 isn’t bad — take a random 20 — though I wouldn’t assign a confidence interval in doing so. The confidence interval would be completely made up.
My thought is that, if we’re starting with 10,000 pennies, select a random 50 and see which is the most recent. Then select another random 50 and see if you get a different result. If not, or if it’s close, then the most recent penny in the sample is probably pretty close to the most recent penny in the entire bar.
No worries. Not only do I identify as female, I have the correct equipment for the venue.
When I went through the I’m-collecting-coins phase as a kid, I deliberately placed two brand new super-shiny pennies in protective sleeves. They are still shiny 50 years later.
On one of those home-building shows in the last couple of years the owner did the encased penny thing as the floor of a shower.
Lucky Clover Irish Pub in Milwaukee?