*"I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the law of frequency of error. The law would have been personified by the Greeks if they had known of it. It reigns with serenity and complete self-effacement amidst the wildest confusion. The larger the mob, the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of unreason." (Sir Francis Galton, 1889)*

*"The central limit theorem says that, under conditions almost always satisfied in the real world of experimentation, the distribution of such a linear function of errors will tend to normality as the number of its components becomes large. The tendency to normality occurs almost regardless of the individual distributions of the component errors. An important proviso is that several sources of error must make important contributions to the overall error and that no particular source of error dominate the rest." **(George E P Box et al, "Statistics for Experimenters: Design, discovery, and innovation" 2nd Ed., 2005)*

*"Two things explain the importance of the normal distribution: (1) The central limit effect that produces a tendency for real error distributions to be 'normal like'. (2) The robustness to nonnormality of some common statistical procedures, where 'robustness' means insensitivity to deviations from theoretical normality." (George E P Box et al, "Statistics for Experimenters: Design, discovery, and innovation" 2nd **Ed., 2005)*

*"Statistical inference is really just the marriage of two concepts that we’ve already discussed: data and probability (with a little help from the central limit theorem)." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)*

*"The central limit theorem tells us that in repeated samples, the difference between the two means will be distributed roughly as a normal distribution." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)*

*"The central limit conjecture states that most errors are the result of many small errors and, as such, have a normal distribution. The assumption of a normal distribution for error has many advantages and has often been made in applications of statistical models."** (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)*

*"The central limit theorem in statistics states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable’s distribution in the population." (Jim Frost)*