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Problem: Suppose you measure three numbers as follows: = 200 § 2; = 50 § 2; = 40 § 2; where the three uncertainties are independent and random. Use step-by-step propagation to find the quantity q = x=(y ¡ z) with its uncertainty.
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Resolution and Uncertainty. Readings are when one value is found e.g. reading a thermometer, measurements are when the difference between 2 readings is found, e.g. a ruler (as both the starting point and end point are judged).
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An error is the difference between the measured value and the expected value of something (unavoidable). An uncertainty is a way of expressing or summarizing the error (unavoidable).
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There are two kinds of error that one deals with in the lab: random error and systemic error. Random error, per the name, are statistical e ects that push your data every which way from the \true" result, with no consistency to its e ects. These will result in your data being right on average, but any individual data point will be o .
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2 Random and Systematic Uncertainty. Measurement uncertainties can be divided into two distinct classes: random (or statistical) errors, and systematic errors.
Introduction. Uncertainties exist in all experiments. The final goal of any experiment is to obtain reproducible results. Knowing errors and uncertainties is an essential part for ensuring reproducibility. To know the uncertainties we use two approaches: Repeat each measurement many times and determine how well the result reproduces itself.
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The process of evaluating this uncertainty associated with a measurement result is often called uncertainty analysis or error analysis. The complete statement of a measured value should include an estimate of the level of confidence associated with the value.
