# Lab 5 is due general formula of error propagation x

• Notes
• 15

This preview shows pages 2–12. Sign up to view the full content.

No LABS . Lab 5 is due.

This preview has intentionally blurred sections. Sign up to view the full version.

General Formula of Error propagation x dx dq q Δ = Δ ) , , ( z y x q q = 2 2 2 ... Ο Π Ξ Μ Ν Λ Δ + + Ο Ο Π Ξ Μ Μ Ν Λ Δ + Ο Π Ξ Μ Ν Λ Δ = Δ z z q y y q x x q q
Typical situation - a sample (set) of N numeric values of the same parameter What are the things we usually want to know? Statistical analysis of data N x N x x x x i N = + + + = ... 2 1 = = N i i x x x N 1 2 2 ) ( 1 σ N x x x x x x ,..., , , , 4 3 2 1 = 1) The mean value: 2) The variance and standard deviation = = N i i x x x N 1 2 ) ( 1 σ

This preview has intentionally blurred sections. Sign up to view the full version.

= = N i i x x x N 1 2 ) ( 1 1 σ standard deviation (correct definition - note N-1 instead of N) Does NOT change significantly with increased N standard deviation of the mean Defines uncertainty of the mean Decreases with increased N (scales as 1/ N) Example: going from N=30 to N=3,000 results in 100 times greater sample or factor 10 improvement in uncertainty of = = = N i i x x x x N N N 1 2 ) ( ) 1 ( 1 σ σ x x
Normal Error Integral

This preview has intentionally blurred sections. Sign up to view the full version.

68% Test Normal Error Integral
Table of Normal Error Integrals: Appendix A of Taylor (p. 287) Normal Error Integral

This preview has intentionally blurred sections. Sign up to view the full version.

t=1
t=1.47

This preview has intentionally blurred sections. Sign up to view the full version.

How do we translate it into the language of the normal distribution?
This is the end of the preview. Sign up to access the rest of the document.
• Spring '11
• shpyrko

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern