Answer to Question #226298 in Physics for Moxie

Question #226298
The following arbitrary measurements are made and the errors sited are the maximum errors A=15.21 +/- 0.01, B=10.82 +/-0.05, C=11.00 +/- 0.03. If D = A+B+C; (a) calculate the maximum error in D (b) If the errors sited are standard errors, calculate the standard error in D
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Expert's answer
2021-08-16T08:37:04-0400

(a) To calculate the maximum error in D, we need to add all errors:


ΔmaxD=0.01+0.05+0.3=0.09.\Delta_\text{max}D=0.01+0.05+0.3=0.09.

(b) Find the mean:


μ=13(0.01+0.05+0.03)=0.03.\mu=\frac13(0.01+0.05+0.03)=0.03.

Find the standard error:


s.e.==(0.010.03)2+(0.050.03)2+(0.030.03)2= =0.02.s.e.=\\=\sqrt{(0.01-0.03)^2+(0.05-0.03)^2+(0.03-0.03)^2}=\\\space =0.02.


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