Points represented in a Q-Q plot are not always diminished when viewed from left to right. If the two distributions compared are identical, the Q-Q diagram follows the line of 45 degrees y-x. If the two distributions agree after the linear transformation of the values in one of the distributions, the Q-Q diagram follows a line, but not necessarily the y-x line. If the general trend of the Q-Q plot is flatter than the y-x line, the distribution represented on the horizontal axis is more dispersed than the distribution represented on the vertical axis. Conversely, the distribution on the vertical axis is more dispersed than the distribution represented on the horizontal axis when the general trend of the Q-Q plot is steeper than the y-x line. Q-Q plots are often arc-shaped or “S”-shaped, indicating that one distribution is tilted relative to the other, or that one of its distributions has heavier tails than the others. The term “probability diagram” sometimes refers specifically to a Q-Q diagram, sometimes to a more general class of plots and sometimes to the less used P-P diagram. The Correlation Coefficient Probability Chart (PPCC chart) is a quantity derived from the idea of Q-Q plots, which measures the consistency of a distribution adjusted with the observed data and is sometimes used as a means of adjusting a data distribution. The choice of the quantiles of a theoretical distribution may depend on the context and the purpose.
A given choice a sample size n is k/n for k -1, …, n, because it is the quantiles that make the distribution of the sample. The last, n/n, corresponds to the percentile – the maximum value of the theoretical distribution, which is sometimes infinite. Other options are the use of (k – 0.5) /n, or rather to clear the dots evenly in the uniform distribution, with k/(n -1).  Many other options have been proposed, both formally and heuristic, based on theory or simulations relevant to the context. Some of these sections are explained in the following subsections. A narrower question is the choice of a maximum (estimate of a maximum population), known as the German reservoir problem, for which there are similar solutions “maximum test, plus deviation”, the simplest m/n – 1. A more formal application of this standardization of distance is done in the maximum estimate of the distance of the parameters. The main step in creating a Q-Q plot is calculating or estimating the amounts to draw. If one or both axes of a Q-Q plot are based on a theoretical distribution with a continuous cumulative distribution function (CDF), all quantiles are clearly defined and can be obtained by inverting the CDF. If a theoretical probability distribution with a discontinuous CDF is one of the two comparative distributions, some of the quantiles may not be defined, so that an interpolated quantil can be represented. If the Q-Q diagram is data-based, several quantum evaluators are used.
The rules for forming Q-Q plots when quantiles are to be estimated or interpolated are called field positions.