# 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
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## There are 146 comments.

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1. Contributor
Internet's Hank
@HankRhody

As a lawyer you’re trained to never ask a question to which you don’t know the answer. Well, I never trained as a lawyer, so I screwed that part up. I know there’s a way to solve this question but I don’t know how to do it myself. On the off chance that there’s no bored statisticians wandering by to explain this to me y’all will have to live with no answer either. Sorry about that.

2. Thatcher
Clavius
@Clavius

I’d go for a year or two after the latest date on the pennies.  Old ones don’t matter.

So how many do you need? It depends on if the selection of pennies for the bar is random.  It is not, the owner could have selected old pennies.  If he selected new pennies, it doesn’t matter, because that would just answer the question.

I’d look for the newest penny.

3. Coolidge
kedavis
@kedavis

Unless you know that the pennies are somehow evenly distributed by year, I don’t think even Fermi can help you.

Or at least, I wouldn’t bet any money on having the right answer.

4. Member
Jimmy Carter
@JimmyCarter

What a coincidence…. I’ve had a barmaid by arranging roughly a hundred bucks.

5. Thatcher
Clavius
@Clavius

Unless you know that the pennies are somehow evenly distributed by year, I don’t think even Fermi can help you.

Or at least, I wouldn’t bet any money on having the right answer.

Irrelevant, the latest penny is the only one needed for dating the making of the bar.  And that was the question.

6. Thatcher
Clavius
@Clavius

So the question is, how many pennies do you have to look at to find the newest penny?

That is a good sampling problem, which, I think, is how you have set this up.

7. Coolidge
kedavis
@kedavis

Unless you know that the pennies are somehow evenly distributed by year, I don’t think even Fermi can help you.

Or at least, I wouldn’t bet any money on having the right answer.

Irrelevant, the latest penny is the only one needed for dating the making of the bar. And that was the question.

Yes, but, as I said, if they aren’t distributed evenly by dates, even picking a few from each part of the bar from end to end won’t really give a good sample.  And you’re not likely to find the newest that way either.

8. Thatcher
Clavius
@Clavius

Yeah, so I totally missed the question.

Focus on the bright ones.

And forgive my denseness in this thread.

9. Contributor
Internet's Hank
@HankRhody

Clavius (View Comment):
It depends on if the selection of pennies for the bar is random.

kedavis (View Comment):
Unless you know that the pennies are somehow evenly distributed by year,

I can tell you it’s not going to be a normal distribution. It’ll have a sharp cut-off with zero pennies newer than the year the bar was made and a long tail of older pennies. That doesn’t mean nothing can be determined about the curve, or that we won’t be able to estimate the year the bar was made from the data available.

10. Member
Not a Gubmint Spy
@OldDanRhody

I recall a case study in my statistics text about how the Allies arrived at an estimate of how many German tanks were produced, based on the serial numbers taken from captured tanks (you could rely on the Germans to not fudge on something so serious as serial numbers).  I’ll take a look, see if it helps.

11. Thatcher
Clavius
@Clavius

Sampling might work.  Look across the whole bar.

(I’ll go have some more wine given my documented failures above.)

12. Member
9thDistrictNeighbor
@9thDistrictNeighbor

There’s a pizza place we go to from time to time that has the same sort of pennies-encased-in-plastic as the floor in the ladies room.  I’ve never looked closely to see the dates on the coins, but the restaurant itself dates from 1968.  Maybe this was a wild and crazy 60’s thing.

13. Member
John H.
@JohnH

Funny, just today I was thinking about the German tank problem. Which, I fear, this isn’t quite.

14. Coolidge
kedavis
@kedavis

Clavius (View Comment):
It depends on if the selection of pennies for the bar is random.

kedavis (View Comment):
Unless you know that the pennies are somehow evenly distributed by year,

I can tell you it’s not going to be a normal distribution. It’ll have a sharp cut-off with zero pennies newer than the year the bar was made and a long tail of older pennies. That doesn’t mean nothing can be determined about the curve, or that we won’t be able to estimate the year the bar was made from the data available.

Well if your sample is a higher percentage of the coins available, sure.  But there are all kinds of ways the pennies could be distributed that would foul you up.

15. Contributor
Internet's Hank
@HankRhody

There’s a pizza place we go to from time to time that has the same sort of pennies-encased-in-plastic as the floor in the ladies room. I’ve never looked closely to see the dates on the coins, but the restaurant itself dates from 1968. Maybe this was a wild and crazy 60’s thing.

The newest penny I saw on the bar in the photo was 2014. Doesn’t mean it wasn’t done as a retro 60’s thing.

I’ll also say I’m a lot more comfortable leaning in for a close look at the counter than I would be scrabbling around the ladies’ room floor.

16. Coolidge
kedavis
@kedavis

There’s a pizza place we go to from time to time that has the same sort of pennies-encased-in-plastic as the floor in the ladies room. I’ve never looked closely to see the dates on the coins, but the restaurant itself dates from 1968. Maybe this was a wild and crazy 60’s thing.

The newest penny I saw on the bar in the photo was 2014. Doesn’t mean it wasn’t done as a retro 60’s thing.

I’ll also say I’m a lot more comfortable leaning in for a close look at the counter than I would be scrabbling around the ladies’ room floor.

Well if you got drunk first, at least you’d have that excuse.

17. Member
Matt Balzer, Imperialist Claw
@MattBalzer

There’s a pizza place we go to from time to time that has the same sort of pennies-encased-in-plastic as the floor in the ladies room. I’ve never looked closely to see the dates on the coins, but the restaurant itself dates from 1968. Maybe this was a wild and crazy 60’s thing.

The newest penny I saw on the bar in the photo was 2014. Doesn’t mean it wasn’t done as a retro 60’s thing.

I’ll also say I’m a lot more comfortable leaning in for a close look at the counter than I would be scrabbling around the ladies’ room floor.

Well if you got drunk first, at least you’d have that excuse.

It was in CA, so they were all “gender-neutral”

18. Member
The Reticulator
@TheReticulator

9thDistrictNeighbor (View Comment):
There’s a pizza place we go to from time to time that has the same sort of pennies-encased-in-plastic as the floor in the ladies room.

And you know this because…???

19. Member
The Reticulator
@TheReticulator

9thDistrictNeighbor (View Comment):
There’s a pizza place we go to from time to time that has the same sort of pennies-encased-in-plastic as the floor in the ladies room.

And you know this because…???

Never mind. I don’t want to misgender anyone here.

20. Member
The Reticulator
@TheReticulator

Internet's Hank: Should I bother taking dates off of the dull pennies

Is that even legal in the U.S.?

21. Member
Sisyphus
@Sisyphus

So the question is, how many pennies do you have to look at to find the newest penny?

That is a good sampling problem, which, I think, is how you have set this up.

All of them, assuming none are from the current year. It only takes one to falsify any earlier date, statisticians be damned.

22. Coolidge
Flicker
@Flicker

Internet’s Hank: Should I bother taking dates off of the dull pennies

Is that even legal in the U.S.?

No, but I know a couple Pennys that would take exception to this characterization.

23. Coolidge
BDB
@BDB

Big believer in the power of limited data plus intelligence to give intelligent informed estimates.

First thing I thought of was the rule of five (because I assume we’re trying to minimize) to get the median age to better than 90% CI, and then find out what the average age of a penny in circulation was, and if it’s comfortably far back in the past (the mode won’t be the median, but how for advanced will the mode be?), use that rule of 5 median, assume something else, and then…

BUT pennies are skewed almost like a power law with a shelf at the recent end– last year’s pennies typically dominate gently over the last maybe ten years, and then it drops expo.

So it took some team 630 pennies to get every one from the past 40 years.  Obviously, it’s the older, not the newer ones that likely were the hardest to get (assume they checked after each penny to see if the collection was complete).

There are 10,000 pennies.  I’ll take the most recent of a randomly selected 20 (assuming the pennies were originally captured representing then-current circulation) and give it a CI of 90%.

24. Coolidge
kedavis
@kedavis

So the question is, how many pennies do you have to look at to find the newest penny?

That is a good sampling problem, which, I think, is how you have set this up.

All of them, assuming none are from the current year. It only takes one to falsify any earlier date, statisticians be damned.

Yeah that’s basically what my argument amounts to also.  I sometimes like to say, the chances of something happening are either zero or 100%, depending on whether or not it happens.

25. Member
Not a Gubmint Spy
@OldDanRhody

Funny, just today I was thinking about the German tank problem. Which, I fear, this isn’t quite.

No, not quite, but with some simplification the method ought to give a reasonable estimate.  After all, how precise does one have to be for a barroom estimate?

Answer: Depends upon the wager, I would think.

26. Coolidge
kedavis
@kedavis

Funny, just today I was thinking about the German tank problem. Which, I fear, this isn’t quite.

No, not quite, but with some simplification the method ought to give a reasonable estimate. After all, how precise does one have to be for a barroom estimate?

Answer: Depends upon the wager, I would think.

Did you see the Cheers episode where “Kramer” (Michael Richards) showed up to collect on a bet that he made with Sam Malone that Sam would marry Jacqueline Bisset?  Well, Sam and the gang checked the phone books and found this girl named Jacqueline Bisset…

27. Coolidge
BDB
@BDB

Unless you know that the pennies are somehow evenly distributed by year, I don’t think even Fermi can help you.

Or at least, I wouldn’t bet any money on having the right answer.

They wouldn’t be evenly distributed by year, but assuming that they were fairly selected, they should be distributed in a tractable menner.

28. Member
Judge Mental
@JudgeMental

Why not just ask?

29. Member
The Reticulator
@TheReticulator

Why not just ask?

If Joe Biden is tending the bar, don’t believe anything he says.

30. Coolidge
BDB
@BDB

Internet’s Hank: Should I bother taking dates off of the dull pennies

Is that even legal in the U.S.?

No, but I know a couple Pennys that would take exception to this characterization.

And some women get by taking pennies off the dull dates.

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