According to Benford’s law, for many data sets the leading digits of individual sample values follow the distribution shown in the first two rows of the following table. In normal and fair badminton play, leading digits in the numbers of rallies tend to follow the distribution of Benford’s law. In a study of leading digits for the numbers of badminton rallies in international tournaments, the frequencies in the bottom row of the table were obtained (based on data from “Preliminary Study to Detect Match-Fixing: Benford’s Law in Badminton Rally Data,” by Park et al., Journal of Physical Education and Sports Management, Vol. 3, No. 1). Does it appear that the observed frequencies fit the distribution from Benford’s law? What does the result suggest about cheating in those matches?

Leading Digit Benford's Law: Distribution of Leading Digits Leading Digits of Numbers of Rallies 1 2 3 4 3679 1515 974 5 6 7 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 898 866 757 8 9 740 743 649