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It is usual to assume that the deviation follows the normal distribution. In practical data analysis, a quantile-quantile plot is a simple way to examine this assumption. A quantile-quantile plot is a plot of ordered values of the data versus the corresponding quantiles of a standard normal distribution, i.e., a normal distribution with mean zero and standard deviation one. Consider a data set {x} that is ranked according to size. The cumulative distribution function is , i.e., the probability that one of the elements is smaller than x. The quantile function is the inverse of the cumulative distribution function. Thus the quantile function gives the percentage points of the distribution. If the distribution of the ordered data exactly follows the normal distribution, the normal probability quantile-quantile plot shows a straight line.
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