Let us start with an example. Suppose that 10 measured data are arranged in increasing order as in (i) (they are assumed to obey the normal distribution). If the data number i is plotted in ordinate and the data value x is plotted in abscissa, one obtains the cumulative plot (ii). In this graph the ordinate is naturally ticked with the spacing of unity. If one adjusts the tick spacing appropriately, one may obtain the plot where the poins are aligned in a straight line as in (iii).

The idea of tick adjustment is not new. For example, Dr. Berendsen gives such plots on pages 7 and 170. But he does not explain the theory behind the adjustment.

Suppose that we have obtained x_min〜x_max, which obey the normal distribution, N(x), characterized by the mean and the standard deviation. Then we can obtain the cumulative plot y=cum(x) as

For x_min=2, x_max=8, a=5, σ=1, A=1.017(A is fixed by the condition cum(x_max)=1 ) we obtain the original cumulative plot (broken line) and adjusted plot (solid line) as shown below. Tick position for 5% is also shown.