Answer to Question #226298 in Physics for Moxie

Question

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

Answer 1

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

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

(b) Find the mean:

$$\mu=\frac13(0.01+0.05+0.03)=0.03.$$

Find the standard error:

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