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发表于 2004-5-6 09:43:51
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< 0cm 0cm 0pt"><FONT face="Times New Roman">The general appearance of the rectangles in Fig.1 is quite striking ,especially the tall hump in the centre and the rapidly falling tails on each side.There are certain minor irregularities in the pattern, and these would, in general ,be more ronounced if the size of the sample were smaller. Conversely, weth larger samples we usually find that the set of rectangles presents a more regular appearance. This suggests that if we had a very large number of measurements ,the ultimate shape of the picture for a suitably small width of rectangle would be something very like a smooth curve,Such a curve could be regarded as representing the true ,theoretical or ideal distribution of heights in a very (or ,better,infinitely)large population of individuals.</FONT></P>< 0cm 0cm 0pt"><FONT face="Times New Roman"> What sort of ideal curve can we expect ? There are seveala theoretical reasons for expecting the so-called Gaussiao or “normal “curve to turn up in practice;and it is an empirical fact that such a curve lften describes with sufficient accuracy the shape of histograms based on large numbers of obscrvations. Moreover,the normal curve is one of the easiest to handle theoretically,and it leads to types of statistical analysis that can be carried out with a minimum amount of computation. Hence the central importance of this distribution in statistical work .</FONT></P>< 0cm 0cm 0pt"><FONT face="Times New Roman"> The actual mathematical equation of the normal curve is where u is the mean or average value and </FONT><v:shapetype><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></v:shapetype><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman"> is the standard deviation, which is a measure of the concentration of frequency about the mean. More will be said about </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">and </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman"> later .The ideal variable x may take any value from </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman"> to </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">.However ,some real measurements,like stature, may be essentially positive. But if small values are very rare ,the ideal normal curve may be a sufficiently close approximation. Those readers who are anxious to avoid as much algebraic manipulation as possible can be reassured by the promise that no derect use will be made in this book of the equation shown. Most of the practical numerical calculations to which it leads are fairly simple.</FONT></P><P 0cm 0cm 0pt"><FONT face="Times New Roman"> Fig. 1 shows a normal curve, with its typocal symmetrical bell shape , fitted by suitable methods to the data embodied in the rectangles. This is not to say that the fitted curve is actually the true, ideal one to which the histogram approxime.tes; it is merely the best approximation we can find.</FONT></P><P 0cm 0cm 0pt"><FONT face="Times New Roman"> The mormal curve used above is the curve we have chosen to represent the frequency distribution of stature for thr ideal or infinitely large population. This ideal poplation should be contrasted with the limited sample of obsrever. Values that turns up on any occasion when we make actual measurements in the real world. In the survey mentioned above we had a sample of 117 men .If the community were sufficiently large for us to collect several samples of this size, we should find that few if any of the corresponding histograms were exactly the same ,although they might all be taken as illustrating the underlying frequency distribution. The differences between such histograms constitute what we call sampling variation, and this becomes more prominent at the size of sample decreases.</FONT></P> |
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发表于 2004-5-6 09:43:36