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Issues with rounding

  1. #1
    Registered User
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    MS-Off Ver
    Excel 2007

    Issues with rounding

    I'm not sure if this is a excel question or a maths one.

    I have three samples:

    Population Number Rate Per 1000 Population
    1000 150 150.000
    2000 160 80.000
    3000 170 56.667

    In excel I've calculated the rate per 1000 by dividing the "number" by the "population" divided by 1000.

    Anyway, I get the rates above. The problem comes with the average for the group. If I used Excel and average all three rate cells I get an overall average of 95.56.

    HOWEVER if I sum the total "population" and the total "number" and divide using the same formula as above (i.e. dividing the "number" by the "population" divided by 1000) then I get 80.00

    Is this Excel rounding numbers in the background? It all seems a bit wierd to me as they should be the same figure surely???

    Many thanks

  2. #2
    Forum Guru shg's Avatar
    Join Date
    The Great State of Texas
    MS-Off Ver
    2003, 2010

    Re: Issues with rounding

    To arrive at the same results, you need to take the population-weighted average of the averages. Take a more extreme example:

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    It should not surprise you that the average of the averages is not the same as percent calculated for the total.
    Entia non sunt multiplicanda sine necessitate

  3. #3
    Administrator FDibbins's Avatar
    Join Date
    Duncansville, PA USA
    MS-Off Ver
    Excel 2000/3/7/10/13/16/365

    Re: Issues with rounding

    As shg said, you cannot take an average of averages, it is not mathematically correct. the only true average in your situation is an average calculated on the total values
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