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.

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  1. Flicker Coolidge
    Flicker
    @Flicker

    Judge Mental (View Comment):

    Why not just ask?

    How do you know that barmaid’s gonna tell you the truth?

    • #31
  2. Flicker Coolidge
    Flicker
    @Flicker

    BDB (View Comment):

    Flicker (View Comment):

    The Reticulator (View Comment):

    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.

    Are we still talking about fruit?

    • #32
  3. Internet's Hank Contributor
    Internet's Hank
    @HankRhody

    BDB (View Comment):

    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%.

    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? 

    • #33
  4. Internet's Hank Contributor
    Internet's Hank
    @HankRhody

    Sisyphus (View Comment):

    Clavius (View Comment):

    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.

    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?

    • #34
  5. Internet's Hank Contributor
    Internet's Hank
    @HankRhody

    Judge Mental (View Comment):

    Why not just ask?

    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.

    • #35
  6. Sisyphus Member
    Sisyphus
    @Sisyphus

    Internet's Hank (View Comment):

    Sisyphus (View Comment):

    Clavius (View Comment):

    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.

    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?

    If it was easy all of those statisticians would find no takers.

    • #36
  7. Percival Thatcher
    Percival
    @Percival

    The only Penny I ever dated was too bright to say ‘yes’ a second time.

    • #37
  8. Flicker Coolidge
    Flicker
    @Flicker

    Internet's Hank (View Comment):

    BDB (View Comment):

    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%.

    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?

    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.

    • #38
  9. Judge Mental Member
    Judge Mental
    @JudgeMental

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    BDB (View Comment):

    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%.

    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?

    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.

    • #39
  10. BDB Inactive
    BDB
    @BDB

    Internet's Hank (View Comment):

    BDB (View Comment):

    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%.

    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?

    Sure, but then you’re just doing two sequential samples.

    • #40
  11. BDB Inactive
    BDB
    @BDB

    Internet's Hank (View Comment):

    Sisyphus (View Comment):

    Clavius (View Comment):

    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.

    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?

    All you have to do is keep the latest year seen so far in mind.

    • #41
  12. Flicker Coolidge
    Flicker
    @Flicker

    Judge Mental (View Comment):

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    BDB (View Comment):

    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%.

    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?

    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.

    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%.

    • #42
  13. Flicker Coolidge
    Flicker
    @Flicker

    BDB (View Comment):

    Internet’s Hank (View Comment):

    Sisyphus (View Comment):

    Clavius (View Comment):

    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.

    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?

    All you have to do is keep the latest year seen so far in mind.

    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.

    • #43
  14. Internet's Hank Contributor
    Internet's Hank
    @HankRhody

    Flicker (View Comment):
    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. 

    • #44
  15. Flicker Coolidge
    Flicker
    @Flicker

    Internet's Hank (View Comment):

    Flicker (View Comment):
    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.  :)

    • #45
  16. kedavis Coolidge
    kedavis
    @kedavis

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    Flicker (View Comment):
    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

    • #46
  17. The Reticulator Member
    The Reticulator
    @TheReticulator

    Internet's Hank (View Comment):

    Flicker (View Comment):
    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 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. 

    • #47
  18. Flicker Coolidge
    Flicker
    @Flicker

    kedavis (View Comment):

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    Flicker (View Comment):
    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

    Well, they could always ask the manager.  Why would he lie?

    • #48
  19. BDB Inactive
    BDB
    @BDB

    Flicker (View Comment):

    kedavis (View Comment):

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    Flicker (View Comment):
    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

    Well, they could always ask the manager. Why would he lie?

    Alright, Karen.

    • #49
  20. Flicker Coolidge
    Flicker
    @Flicker

    BDB (View Comment):

    Flicker (View Comment):

    kedavis (View Comment):

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    Flicker (View Comment):
    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

    Well, they could always ask the manager. Why would he lie?

    Alright, Karen.

    Excuse me?

    • #50
  21. BDB Inactive
    BDB
    @BDB

    Flicker (View Comment):

    BDB (View Comment):

    Flicker (View Comment):

    kedavis (View Comment):

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    Flicker (View Comment):
    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

    Well, they could always ask the manager. Why would he lie?

    Alright, Karen.

    Excuse me?

    Karen always wants to talk to the manager.

    • #51
  22. Internet's Hank Contributor
    Internet's Hank
    @HankRhody

    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.

    • #52
  23. Flicker Coolidge
    Flicker
    @Flicker

    BDB (View Comment):

    Flicker (View Comment):

    BDB (View Comment):

    Flicker (View Comment):

    kedavis (View Comment):

    Flicker (View Comment):

    Internet’s Hank (View Comment):

    Flicker (View Comment):
    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

    Well, they could always ask the manager. Why would he lie?

    Alright, Karen.

    Excuse me?

    Karen always wants to talk to the manager.

    Oh.  I guess so.

    • #53
  24. Internet's Hank Contributor
    Internet's Hank
    @HankRhody

    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.

    • #54
  25. Flicker Coolidge
    Flicker
    @Flicker

    Internet's Hank (View Comment):

    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.

    Oops.

    • #55
  26. Matt Bartle Member
    Matt Bartle
    @MattBartle

    Internet's Hank (View Comment):
    the bartender had a tremendous pair of knockers

    And you’re looking at the pennies??

     

    • #56
  27. Jerry Giordano (Arizona Patriot) Member
    Jerry Giordano (Arizona Patriot)
    @ArizonaPatriot

    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.

    • #57
  28. 9thDistrictNeighbor Member
    9thDistrictNeighbor
    @9thDistrictNeighbor

    The Reticulator (View Comment):

    The Reticulator (View Comment):

    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.

    No worries.  Not only do I identify as female, I have the correct equipment for the venue.

    Flicker (View Comment):
    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.

    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.

    • #58
  29. Full Size Tabby Member
    Full Size Tabby
    @FullSizeTabby

    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. 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.

    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. 

    • #59
  30. Charlotte Member
    Charlotte
    @Charlotte

    Lucky Clover Irish Pub in Milwaukee?

    • #60
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