Results 1 to 7 of 7

Math Help - Odd Ratio calculation - Give to Take

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    4

    Odd Ratio calculation - Give to Take

    I have a list of people, each who give a certain amount of X. Occasionally they receive a certain number of Y for their troubles.

    I'm looking for a formula that will let me sort a list of people based on the ratio of X to Y.

    In other words, if:
    Jim gave 10x and got 1y
    Sara gave 10x and got 2y
    Chip gave 1x and got 0y, and
    Deb gave 3x and got 2y
    I need to be able to sort them Jim, Sara, Chip, Deb.

    Part of the trouble I'm encountering here is the division by 0 for Chip. Does anyone have any nifty suggestions for a formula that I can apply to a list like this, but of about 50 people?

    Thank you, in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,113
    Thanks
    325
    You calculate the ratio of x to y by simply dividing teh x quantity by the y quantity. You can then sort the results in order from highest to lowest ratio. For example, Jim's ratio is 10/1 = 10, and Sara's is 10/2 = 5, so you would place Jim above Sara. As for Chip, his ratio is 1/0 =  \infty , so he goes above Jim. Can you figure out where Deb belongs on the list?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    4
    I had approached it that way originally, but the circumstance of the list should reflect Jim at the top, because he's given a lot of X, and hasn't received much Y in reward. Chip has only given 1 X, so shouldn't be above him on the list.

    I suppose it's not really the basic ratio I'm after here, but how would one describe a formula that reflects what I noted above?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,113
    Thanks
    325
    Here's a thought - from the data you can calculate an average value for the ratio of Y to X, which you can think of as the "expected" payback for giving X. For the 4 data points you provided, the average ratio of Y/X is 0.242, so for every X a person gives the average return is 0.242 Y. Then look to see how each person's actual return of Y differs from the expected return. What you find is this:

    Calculations of actual - expected:
    Jim: 1 - 0.242*10 = -1.42
    Sara: 2 - 0.242*10 = -0.42
    Chip: 0 - 0.242*1 = -0.242
    Deb: 2- 0.242*3 = +1.274

    If someone received the expected amount this formula gives 0. A negative number means you got less Y than average, and a positive number means you got more in return for your X. From this Jim got a lot less Y than he should have expected, and Deb got a lot more.

    Does this help?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2010
    Posts
    4
    I think you've got it! That's exactly it - I need determine the average of the ratios, then sort by relation to the average for each person on the list.

    Thank You!! I'll post back when I can confirm that I've got my head around this correctly ;}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,113
    Thanks
    325
    I think the approach I suggested does exactly what yo're looking for. Next time there's some Y available, give it to Jim, and he will become even with Sara. After each "gift" of Y to an individual, you resort the list. You may have to define some tie breaker rules though.

    And it's Deb who's the weasel, not Chip!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2010
    Posts
    4
    lol - Fix'd! - and indeed, Thank You
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. What does this calculation give me in trading?
    Posted in the Business Math Forum
    Replies: 0
    Last Post: October 17th 2011, 09:59 AM
  2. Replies: 7
    Last Post: October 28th 2010, 08:40 AM
  3. calculation of ratio with random error
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: October 11th 2010, 07:44 AM
  4. Ratio for curve and point-ratio form
    Posted in the Algebra Forum
    Replies: 4
    Last Post: January 11th 2010, 12:07 AM
  5. Finding n given the ratio of nCr to another ratio
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 5th 2009, 07:03 PM

Search Tags


/mathhelpforum @mathhelpforum