One of the important actions that is in nearly all of the foregoing chapters is measurement. We measure time, coordinates, proper motions, parallaxes, magnitudes, the positions of lines in spectra, and shifts in positions of spectral lines, for example. After a measurement has been made we want to know how good the measurement really is, and in order to evaluate our measurements, we must turn to statistics. We would also like to use our measured data to make predictions either within or beyond the range of the measurements. Here we shall describe some of the principles that permit us to achieve these two goals in practical situations.
As an example, let us assume that a student is asked to determine the position of a spectrum line by measuring the distance from some reference position to the line center with a ruler. The smallest divisions on the ruler are one mm apart. We should be able to read the position of the line to within one tenth of a millimeter (0.1 mm). Just as a check the student makes a second setting and reads a new value with the ruler. She tries again and again until she has made fifty tries, and she never makes quite the same reading twice. Which of these many readings should be adopted as the correct one?
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