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Unformatted text preview: Chemistry 15 Lecture 2 Reading Assignment this week: Chapter 3 & 4 January 28, 2008 Statistical Analysis of Data I
a) b) c) Systematic vs. random errors Precision vs. accuracy Statistical methods work wonders but only when experiments are burdened solely with random errors Distribution of error: Gaussian curve • results close to the true value are most probable • probability of results high and low is equal and decreases exponentially • width of the gaussian curve is measured in units of standard deviation σ. • standard deviation represents precision of the experiment Mean value (statistical average) is the best approximation of the true value d) e) x= ∑x
i =1 N i N μ = lim x( N )
N →∞ f) Standard deviation is a measure of precision (μ ± σ contains 68.3% of all results)
⎛N ⎞2 ∑ ( xi − x)2 ⎟ ⎜ ⎟ s = ⎜ i =1 ⎜ N −1 ⎟ ⎜ ⎟ ⎝ ⎠
1 σ = lim s ( N )
N →∞ g) Confidence interval
μ = xi ± 1.96 σ
μ = x( N ) ±
1.96 σ N μ = x( N ) ± ts N ...
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