This sandbox was generated by Claude (Anthropic) for the STAT-101 course materials. Almost everything on it is really simulated in your browser. Every parent distribution is sampled by real inverse-transform or mixture draws from a seeded generator; every histogram is a real count of real draws; the median and the maximum are real order statistics; the variance statistic is the real unbiased sample variance with the n−1 divisor; the skewness and excess kurtosis are computed from the statistics that were actually drawn. There is no drawn bell curve anywhere except the two curves explicitly labelled theory, which come from closed forms and are dashed so you can tell them apart from the bars. The Model self-check box compares the simulation's measured numbers against those closed forms, live, so you can see it is not lying to you.
Two published algorithms are named rather than hidden. The inverse normal CDF used by the Q–Q plot is Acklam's rational approximation, refined by two Halley steps against an erfc computed from a series and a continued fraction, so its quantiles are accurate to about 1 part in 1015; the Q–Q plotting positions are Blom's (i − 0.375)/(R + 0.25), and the straightness number beside the plot is a probability-plot correlation coefficient in the sense of Filliben. A normal quantile with no stated algorithm is not reproducible, so this page states one.
Two numbers are illustrative and say so where they are used. The default knob values, and the PPCC threshold 0.9990 that the “how large is large enough” search uses to declare a sampling distribution normal-looking. There is no canonical threshold; move it and the answer moves. That is the point of showing it rather than printing n ≥ 30 and stopping.
Inverse normal CDF: P. J. Acklam, “An algorithm for computing the inverse normal cumulative distribution function” (rational approximation, relative error < 1.15×10−9 before refinement). Plotting positions: G. Blom, Statistical Estimates and Transformed Beta Variables, Wiley, 1958. Probability-plot correlation coefficient: J. J. Filliben, “The probability plot correlation coefficient test for normality,” Technometrics, vol. 17, no. 1, pp. 111–117, 1975. Seeded generator: mulberry32 (public domain).
No number on this page came from a dataset. There is no real data in this repository and inventing some would be the worst thing this page could do. Everything you see is a simulation of a distribution whose true parameters are printed beside it.
Course demo — linked from the lesson deck in both languages; the page itself is English‑only for now. Built for STAT-101 Module 4, Lesson 4.4 and the Module 4 Distribution Explorer lab. Pick a parent population, pick a sample size n, and the page draws thousands of samples of size n, computes a statistic on each one, and builds the sampling distribution of that statistic in front of you. Everything is recomputed from a seeded generator, so the same settings always draw the same picture. Then switch the parent to Cauchy, or the statistic to maximum, and watch the theorem stop working.