Chebyshev's Rule establishes a lower bound on the fraction of points in a sample lying within standard deviations of the mean of the distribution. This lower bound exists regardless of the distribution from which the sample is drawn. This Demonstration challenges you to defeat Chebyshev's Rule. Click the graphic to create sample points. Then adjust the "examination range" slider to see if you can find any example for which the actual fraction of points within the gray rectangle that represents the range is less than the amount guaranteed by Chebyshev. Having trouble? Increase Chebyshev's handicap until you are able to "beat Chebyshev."
Only the ‐value of the data is examined. The data is spread vertically to facilitate visualization of distinct data points.