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Math Help - Determing Value of "jar" of Coins

  1. #1
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    Determing Value of "jar" of Coins

    Hi everyone. I have been creeping the forums for a little while now and love it.

    I have been having this problem for a while and i was hopping to get some direction.

    I am trying to determine with a fairly high problilty the total value of a "jar of coins" Now it is NOT actually a jar or coins. I am looking at boxes of coins with high values ($1000+).

    I have/get values for the box weights, The box weights inlcuding coins, and the total(exact) value of the coin values/coin count breakdowns.

    I also have weights each individual coin. Now the values of each box will be fairly static. meanign that each box is holds money from a specific location. So what i am thinking is that because of this I can use historical values (coin totals, weights) to create a correlative value for each location.

    Am i on the right track? it has been stumpping me for a while and i want the answer

    Thanks
    Last edited by mr fantastic; July 17th 2009 at 08:34 PM.
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  2. #2
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    Quote Originally Posted by Rayford Booth View Post
    Hi everyone. I have been creeping the forums for a little while now and love it.

    I have been having this problem for a while and i was hopping to get some direction.

    I am trying to determine with a fairly high problilty the total value of a "jar of coins" Now it is NOT actually a jar or coins. I am looking at boxes of coins with high values ($1000+).

    I have/get values for the box weights, The box weights inlcuding coins, and the total(exact) value of the coin values/coin count breakdowns.

    I also have weights each individual coin. Now the values of each box will be fairly static. meanign that each box is holds money from a specific location. So what i am thinking is that because of this I can use historical values (coin totals, weights) to create a correlative value for each location.

    Am i on the right track? it has been stumpping me for a while and i want the answer

    Thanks
    Incomprehensible, try to be clearer, possibly giving an example.

    CB
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  3. #3
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    Updated Explination with example

    Ok here is another go at what i am looking for.

    I am trying to determine the amount(Value) of money(coins)(the majority being 0.25 and higher. Money i would like to deal with is Canadian and American but primarly Canadian. So 0.25, 1.00, 2.00 coins are the MAJOR majority but there is also 0.01, 0.05 and 0.10 coins) inside a container based on weight.

    Each container is filled with money once a week (Monday to friday)(not always on the same day but 95%+ of the time it is the same day of the week). The container holds money from the same location each week.


    There is three sets of data that I have avaliable to help determine the value. I have historical container weights, I know the individual container weight. I also have the actual coin counts from the historical containers. Meaning I know the weight and i know exactly how much money was inside of the container broken down into exact coin type counts.

    I do not have all coin counts for historical data and I would like to be able to determine container value in the future as I cannot always get exact count. So What i want to be able to do i determine the value of the container based on weight hopefully using historical data to increase the probability

    Here is some sample data of what i have avaliable (actual numbers):

    Container is 9.5 to 10 pounds

    Container 1:
    0.01: $0.60
    0.05: $14.80
    0.10: $37.00
    0.25: $7,307.00
    1.00: $11,314.00
    2.00: $16,088.00
    Grant Total: $34,761.40

    Total Weight of Container 1 (Container and Money weighed as one, not a calculated value): 929.09 pounds.

    let me know if you need anymore information

    Edit: Oh if there sample is to large i have a few examples of smaller container values
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Rayford Booth View Post
    Ok here is another go at what i am looking for.

    I am trying to determine the amount(Value) of money(coins)(the majority being 0.25 and higher. Money i would like to deal with is Canadian and American but primarly Canadian. So 0.25, 1.00, 2.00 coins are the MAJOR majority but there is also 0.01, 0.05 and 0.10 coins) inside a container based on weight.

    Each container is filled with money once a week (Monday to friday)(not always on the same day but 95%+ of the time it is the same day of the week). The container holds money from the same location each week.


    There is three sets of data that I have avaliable to help determine the value. I have historical container weights, I know the individual container weight. I also have the actual coin counts from the historical containers. Meaning I know the weight and i know exactly how much money was inside of the container broken down into exact coin type counts.

    I do not have all coin counts for historical data and I would like to be able to determine container value in the future as I cannot always get exact count. So What i want to be able to do i determine the value of the container based on weight hopefully using historical data to increase the probability

    Here is some sample data of what i have avaliable (actual numbers):

    Container is 9.5 to 10 pounds

    Container 1:
    0.01: $0.60
    0.05: $14.80
    0.10: $37.00
    0.25: $7,307.00
    1.00: $11,314.00
    2.00: $16,088.00
    Grant Total: $34,761.40

    Total Weight of Container 1 (Container and Money weighed as one, not a calculated value): 929.09 pounds.

    let me know if you need anymore information

    Edit: Oh if there sample is to large i have a few examples of smaller container values
    You have a number of data points (W_i, V_i),\ i=1,...n of historical container weights and values.

    You want a model that will tell you the estimated value from the weight of a container for which you know only the weight.

    There may be some detail missing from my description above, but this looks like a regression problem (start assuming its linear, if that is not satisfactory we will devise a better assumption by looking at the actual data).

    CB
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  5. #5
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    My math is a little rusty in the regression area. Can you explain a little more for me please?

    Also If i understand your explanation, I have historical data and i assume you mean i can match the weight to the linear curve for approximate container value. I was thinking more of the direction of what happens to approx the value of a jar of coins through sampling. Would sampling of past data work?

    My problem with the linear curve method is wont it cause fairly radical differences if the values are not fairly constant?
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  6. #6
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    Quote Originally Posted by Rayford Booth View Post
    My math is a little rusty in the regression area. Can you explain a little more for me please?

    Also If i understand your explanation, I have historical data and i assume you mean i can match the weight to the linear curve for approximate container value. I was thinking more of the direction of what happens to approx the value of a jar of coins through sampling. Would sampling of past data work?

    My problem with the linear curve method is wont it cause fairly radical differences if the values are not fairly constant?
    This is again virtually incomprehensible.

    Google for linear regression or look up the Wikipedia article on it.

    One thing you should do is draw a scatter plot of the historical data (that is a plot with weight as the horizontal axis and value as the vertical axis, and on the plot mark in some or all of the historical points)

    CB
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  7. #7
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    I know you are saying this is virtually incomprehensible. But besides a few little verbal tangents in my last post i think it still says what i wanted it to say.

    You are saying that i graph the historical weights and cash points to create a graph that would allow me to create a baseline for comparison. The issue i saw with this was that would it not allow for radical and large errors in the weight is drastically different?

    With using the jar of coins method i have read about people would sample from the jar a random sample of coins and use that to determine a probable count percentage of each coin inside of the jar. From this they would calculate the probable coin count based from the total weight of the coin (total weight of jar with coin minus the jar weight), the sample taken from the jar, and the weight of each individual coin type.

    My thinking was i could use the same process. THe only difference was that i would use the historical coin counts (maybe avg of coin counts) as the "container" for the sample to be taken from. (As i cannot take the sample from the container i have weights for). Would this work or is there a math principle i am missing?

    THanks
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  8. #8
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    Oh, Also would more data points in the example be more helpful.

    I graphed the dataset and come up with a R2 value of anywhere from .82 to .95. Is there something i can do it increase accuracy of the line of best fit?
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  9. #9
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    Quote Originally Posted by Rayford Booth View Post
    Oh, Also would more data points in the example be more helpful.

    I graphed the dataset and come up with a R2 value of anywhere from .82 to .95. Is there something i can do it increase accuracy of the line of best fit?
    That level of r^2 is pretty good. If all you are going to measure is the weight The only way to improve the fit of the model to the data is to change the model. It might be that a non-linear model might be better, but I really can't tell you how to proceed without seeing the data, exploratory data analysis is not reducable to a set of rules.

    CB
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  10. #10
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    How much data do you need to see?

    My concern/thinking here is that the coin values can cause many different values. For example a box of 0.25 and a box of 1.00 coins can have a similar weight but be very different in value.

    While the R2 value is pretty good, it leaves a very large variance when dealing with money. Could be a variance of over 1000 dollars. Which i see to be unacceptable
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