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Homework Help: Error Propagation calculation

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Estimate the absolute and relative standard deviations of the following calculations. The number in parentheses is the standard deviation of the preceding value.

    a) z=5.64(s=0.14)*log(138)(s=3)

    2. Relevant equations
    Sx/x =SQRT((Sp/P)2+(Sq/q)2+(Sr/R)2

    Sx=0.434(Sp/P)

    3. The attempt at a solution

    I thought of two ways to go about the problem I am not sure which way is correct here are both attempts:

    log(138)= 2.139
    Z=12.069
    SZ=SQRT((0.14/5.64)2+(3.0/2.139)2)=1.40
    Z=12.07 LaTeX Code: \\pm 1.40

    RSD=(1.4/12.07)*100 =11.6%

    Or my other attempt:

    Z=12.07
    (0.14/5.64)2+(0.434*(3.0/138))=0.01
    Z=12.07LaTeX Code: \\pm 0.01
    RSD=(0.01/12.07)*100=0.08%

    Are either of these ways correct? Any help would be appreciated. Thanks.
     
  2. jcsd
  3. Oct 27, 2008 #2

    LowlyPion

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    Homework Helper

    I would choose a different approach. For:

    z=5.64(s=0.14)*log(138)(s=3)

    Certainly the RSS of the relative uncertainties is a good method. But in that regard I would prefer to treat the relative error of the 3/138 as really the relative uncertainty of the range of Log(138 ±3) which looks to me more like 2.14±.01, because that is the effect on the final result, as opposed to the 3/138.

    Then I would choose to take the RSS of these relative terms according to the product rule.

    ((.14/5.64)2 + (.01/2.14)2)1/2

    And calculate the absolute uncertainty from that expression.
     
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