. Elements of statistics. Statistics. Sec. RECTIFICATION OF THE NORMAL CURVE 103 merit of either, or both, x and y so that the new graph of ?/ = /(.r) becomes a straight line. That is, a curved line is straightened out by a change of scale. Because the reader is assumed to be familiar with logarithms, the description of a method for rectifying a normal curve will be pre- ceded by a similar discussion regarding logarithmic and exponential curves, li Y — logio X, as in Table for selected A^'s, the pairs of values (X, Y = logio X) plot on the curve of Figure TABLE Some Pairs o
. Elements of statistics. Statistics. Sec. RECTIFICATION OF THE NORMAL CURVE 103 merit of either, or both, x and y so that the new graph of ?/ = /(.r) becomes a straight line. That is, a curved line is straightened out by a change of scale. Because the reader is assumed to be familiar with logarithms, the description of a method for rectifying a normal curve will be pre- ceded by a similar discussion regarding logarithmic and exponential curves, li Y — logio X, as in Table for selected A^'s, the pairs of values (X, Y = logio X) plot on the curve of Figure TABLE Some Pairs op Numbers Which Satisfy the Equation Y = logio X X Y X Y X Y 1 100 500 3 150 600 8 200 700 10 250 800 40 300 900 50 350 1000 70 400 100 200 300 400 500 600 700 800 900 1000 X Figure Graph of Y = fog^Q X for X in the interval 1^X^1000. It is obvious that as the size of X increases, the size of Y = logio X increases less and less for equal increases in A". For example, when A changes from 500 to 600, log A changes by ; but when A changes from 900 to 1000 (another increase of 100), log X changes by only It is typical of straight-line (linear) mathe- matical relationships that Y changes the same amount for equal increases in A^. In other words, Y changes uniformly with increas- ing X. If log A is put on a uniform scale, as in Figure , and. 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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