Physics I Lab Manual 2011 14

Physics I Lab Manual 2011 14 - in a calculated quantity we...

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EXPERIMENT 1. STATISTICS equal. The uncertainty in a measured value is not determined by how close the measurement is to some expected value. Figure 1.2: Histogram showing the distribution of ages for students in a class Often we have to calculate a quantity from a measured value (for example calculate the area of a room from measurements of its length and width). When calculating a quantity from a measured value the uncertainty in the measured value causes uncertainty in the calculated quantity. To determine how the uncertainty in a measured quantity affects the uncertainty
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Unformatted text preview: in a calculated quantity we use calculus. If we measure a quantity x and wish to use it to compute a value f ( x ) we can use the fact that the derivative df ( x ) dx gives the relationship between a change δx , and the corresponding change δf , according to δf = df ( x ) dx δx , so letting δx be the uncertainty in the measured quantity x , δf is the uncertainty in the calculated quantity f ( x ). Appendix B described how the uncertainty in a value calculated from several measured quantities is determined. 4...
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