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Thread: numbers in 2 equivalent series

  1. #1
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    numbers in 2 equivalent series

    Here are numbers in 2 series:

    series A: 0, 25, 50, 100, 150, 200

    series B: 0, 20, 33 1/3, 50, 60, 66 1/3

    The numbers shown are just a sample of the numbers in the 2 series. The series are equivalent: for any 2 numbers x and y, the series A value is (y-x)/x, and the series b value is (y-x)/y.

    I canít figure out the formula that would give me the equivalent in series B of any number in series 1 (or vice versa). Can anyone help? Thanks in advance.
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  2. #2
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    Re: numbers in 2 equivalent series

    I have no clue what you are saying.
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  3. #3
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    Re: numbers in 2 equivalent series

    Sorry to be unclear.

    Let's say I want to find out what number in series B corresponds to, say, the number 30 in series A. Is there a formula that would give me the answer (which happens to be 23.0769...)?
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  4. #4
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    Re: numbers in 2 equivalent series

    If the number in the series A is given by (y- x)/x, for some x and y, and the corresponding number for series B is (y- x)/y, then given that the number in the series A is (y- x)/x= A, y- x= Ax and y= (A+ 1)x. So the corresponding number in series B is (y- x)/y= ((A+1)x- x)/(A+1)x= (Ax+ x- x)/(A+ 1)x= Ax/(A+1)x= A/(A+ 1).

    So if the number in series A were 30, the number in series B would 30/31, not 23.0769.... How did you get that number?
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    Re: numbers in 2 equivalent series

    OK, very sorry, I think I need to clarify further.

    The numbers that I'm using in series A and B are percentages. (Not sure if that changes the fundamental logic of all this.)

    So if the number in series A is 30%, the number in series B will be 23.0769...%.

    An example of x and y that produces these results is x=100 and y=130.
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  6. #6
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    Re: numbers in 2 equivalent series

    Quote Originally Posted by Michael56 View Post
    Here are numbers in 2 series:
    series A: 0, 25, 50, 100, 150, 200 & series B: 0, 20, 33 1/3, 50, 60, 66 1/3
    The numbers shown are just a sample of the numbers in the 2 series. The series are equivalent: for any 2 numbers x and y, the series A value is (y-x)/x, and the series b value is (y-x)/y.
    Quote Originally Posted by Michael56 View Post
    The numbers that I'm using in series A and B are percentages. (Not sure if that changes the fundamental logic of all this.) So if the number in series A is 30%, the number in series B will be 23.0769...%. An example of x and y that produces these results is x=100 and y=130.
    To Michael56; Why not just post the exact problem you are trying to solve? If you are not trying to hid something, most of us here are trained to formulate solutions to well posed questions. So tell us the exact question.
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  7. #7
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    Re: numbers in 2 equivalent series

    OK, I was hoping to make things clearer by simplying the problem. But at the risk of making this more muddy, here’s a full explanation.

    I am tracking the performance to 2 investments daily.

    On 3 consecutive days this week:

    Investment 1 is up 8.1%, 8.3%, 8.4%. (The numbers reflect percentage increases from a baseline more than a year ago.)

    Investment 2 on the same days is up 12.9%, 12.9%, 13.1%.

    By applying the first formula mentioned in my original post, investment 2 is better by 59%, 56% and 55% on those days respectively. The formula is (y-x)/x. E.g. (12.9%-8.1%)/8.1%=59%. (Ignore rounding errors. All figures here and below are rounded by my spreadsheet.)

    By applying the second formula, which is a different measure of comparison, investment 2 is better by 37%, 36% and 35%. The formula is (y-x)/y. E.g. (12.9%-8.1%)/12.9%=37%.

    So those 2 series, which I identified as series A and B, are equivalent but different measures of performance. Series A: 59%, 56%, 55%. Series B: 37%, 36%, 35%. There are many more numbers in each series, all derived by the 2 formulas.

    What I want is another formula that will let me plug in any potential series A number and find out its equivalent in series B.

    I.e. I know that 100 in series A is exactly equivalent to 50 in series B. And 25 in series A is exactly equivalent to 20 in series B. (I gave more examples in my OP.) But what is, say, 62.654 in series A equivalent to in series B?

    Worse? Better?
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  8. #8
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    Re: numbers in 2 equivalent series

    Then what Hallsofivy told you above should work.

    A/(A+1)

    $\displaystyle \dfrac{.59}{1.59}\approx .37=37\%$

    .62654/1.62654 - Wolfram|Alpha Results
    Thanks from HallsofIvy
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  9. #9
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    Re: numbers in 2 equivalent series

    The other direction: A=B/(1-B)
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    Re: numbers in 2 equivalent series

    Fantastic! That is precisely what I was looking for.

    Many thanks for your help. Much appreciated.

    Michael
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  11. #11
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    Re: numbers in 2 equivalent series

    Is that all you guys do in Toronto Michael?!

    Which movie best represents all the money that Kathleen Wynne is wasting?

    "Gone with the wind" !!
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