. Elements of statistics. Statistics. 104 BINOMIAL AND NORMAL DISTRIBUTIONS Ch. 4 the corresponding A''s matched with their logarithms, the X-scale is what is called a logarithmic scale. Figure shows the effect of graphing Y = log X against .Y when X is on a logarithmic scale. Uniform scale, logX: Corresponding X: 1 I 2 I 3 4 I 5 I I I 6 7 8 9 10 Figure Matching of the logarithmic and the arithmetic scales of a measm-ement, 10 100 X on logarithmic scale 1000 Figure Graph of Y = log^Q X when X is scaled according to the log^Q X as
. Elements of statistics. Statistics. 104 BINOMIAL AND NORMAL DISTRIBUTIONS Ch. 4 the corresponding A''s matched with their logarithms, the X-scale is what is called a logarithmic scale. Figure shows the effect of graphing Y = log X against .Y when X is on a logarithmic scale. Uniform scale, logX: Corresponding X: 1 I 2 I 3 4 I 5 I I I 6 7 8 9 10 Figure Matching of the logarithmic and the arithmetic scales of a measm-ement, 10 100 X on logarithmic scale 1000 Figure Graph of Y = log^Q X when X is scaled according to the log^Q X as derived from Figure As can be seen, the graph is a straight line, and, for any equal dis- tance along the horizontal axis, the Y changes by the same amount. It is noted that the A'-axis falls into parts of equal length: one for numbers from 1 to 10, one for numbers from 10 to 100, and another for X's between 100 and 1000. This corresponds to numbers whose logarithms have characteristics of 0, 1, and 2, respectively. Graph paper with one scale logarithmic and the other arithmetic will be called semi-log paper. When it has three repeated sections along one axis (X-axis in Figure ) it is called three-cycle semi-log paper. The three cycles correspond to any three successive char- acteristics of logarithms, that is, to numbers which fall between any three successive powers of 10. Figure illustrates the use of semi-log paper to rectify an exponential curve. In this case Y = 2e^-^, but any base for the power could be used. Clearly logio Y — logio 2 + 3X logio e; or. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Fryer, Holly Claire. Wiley
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