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Physics II workshop_Part_66

Physics II workshop_Part_66 - Standard Deviation The...

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134 Standard Deviation The Gaussian is asymptotic to the axis (infinitely wide). We need a method to specify the relative widths of the curves. The standard deviation, s x or σ , is a measure of the width of the curves. The horizontal line shows the standard deviation (from the center to where the line crosses the curve.) We can represent the curve by a shaded box. It is darkest in the middle where most measurements occur, and fades out to zero as we go away from the center. Approximately 2/3 of the measurements lie within 1 standard deviation of the center. If we go two standard deviations out, 95% of the measurements are accounted for. 0 1 2 3 4 5 6 Comparing numbers. Suppose we have four measurements: A (3.8 ± 0.5) cm, B (5.1 ± 0.5) cm, C (3.8 ± 0.2) cm, D (5.1 ± 0.3) cm. These are shown in the diagram to the right. If we don’t have the standard deviations we can only say that the measurements are close. With standard deviations we can say that A and B are equal within uncertainties. That is within 2 σ , A ranges from 2.8 to 4.8 cm
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