Physics II workshop_Part_69

Physics II workshop_Part_69 - Uncertainties and Graphs...

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140 Uncertainties and Graphs: Error Bars (a) Error Bars Data that you plot on a graph will have experimental uncertainties . These are shown on a graph with error bars , and used to find uncertainties in the slope and intercept. In this discussion we will describe simple means for finding uncertainties in slope and intercept; a full statistical discussion would begin with "Least Squares Fitting." Consider a point with coordinates X ± Δ X and Y ± Δ Y. (a) Plot a point, circled, at the point (X,Y). (b) Draw lines from the circle to X + Δ X, X - Δ X, Y + Δ Y, and Y - Δ Y and put bars on the lines, as shown in Figure 6(a). These are called error bars . (c) The true value of the point is likely to lie somewhere in the oval whose dimension is two deviations, i.e. twice the size of the error bars. The oval shown in Figure 6(c) shows the uncertainty region (at 95% confidence--this is statistics speak). It is not usually drawn on graphs. Often the error bars may be visible only for the ordinate (vertical), as
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Physics II workshop_Part_69 - Uncertainties and Graphs...

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