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SOLUTION TO EXERCISE 3
A graph is useful in this situation. The graph should have "number of measurements" on the vertical axis, and "luminosity" on the horizontal axis. (a) The mean value of the luminosity measurements is about 208 units. This is also about the place where the most measurements are, which is around 210 units; this agreement gives us additional confidence So the best estimate of the luminosity of Venus is about 208 units. (b) The bell curve that best fits the distribution of measurements is about 30 measurements high at 208 units; so the half-maximum level is 15 measurements. The bell curve intersects 15 at about 195 units and 225 units; so the full-width at half maximum (FWHM) is about 30 units. Remember that you're measuring the width of the bell curve, and not necessarily the width of the data point distribution. (c) The margin of error is +/- half of the FWHM, that is 15 units. This is a ratio of 208 +/- 15 units, or +/- (15/208) or +/- 7.2 percent. |