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“weight factors” w 1 w 2 etc you already know

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Unformatted text preview: “weight factors” w 1 , w 2 etc: You already KNOW this – e. g. your grade: % 25 5 * % 15 % 25 % 15 + × + × = ∑ FINAL LABS GRADE Weights: 25 for Final Exam, 15 for each of 5 labs More precise data points should carry more weight! Idea: weigh the points with the ~ inverse of their error bar 5 10 15 20 25 x 10 20 30 y(x) Weight-adjusted average: How do we average values with different uncertainties? Student A measured resistance 100±1 Ω (x 1 =100 Ω , σ 1 =1 Ω ) Student B measured resistance 105±5 Ω (x 2 =105 Ω , σ 2 =5 Ω ) 2 1 2 2 1 1 w w x w x w x + + = 2 1 1 1 σ = w 2 2 2 1 σ = w N N N i i i w w w x w x w x w w x w x + + + + + + = = ∑ ∑ ... ... 2 1 2 2 1 1 Or in this case calculate for i=1, 2: with “statistical” weights: BOTTOM LINE: More precise measurements get weighed more heavily! 5 10 15 20 25 x 10 20 30 y(x) How good is the agreement between theory and data? χ 2 TEST for FIT (Ch.12) ( ) ( ) ∑ = − = N j j j j x f y 1 2 2 2 σ χ 5 10 15 20 25 x 10 20 30 y(x) χ 2 TEST for FIT (Ch.12) N N y y = ≅ 2 2 σ σ d 2 2 ~ χ χ = d = N - c # of degrees of freedom # of data points # of parameters calculated from data...
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“weight factors” w 1 w 2 etc You already KNOW this –...

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