This exercise utilized statistical software, in this case SAS, to show that distributions that do not conform to the criterion set forth by the central limit theorem can be modified to still possess the properties and freedom afforded through the central limit theorem via trimming the tails of the distribution. The Cauchy distribution has an infinite mean and variance. Therefore, the measure of central tendency recommended to describe the distribution is the median. However, if we trim the tails of the ordered sample means, then the mean of this new distribution is very close to the median of the original Cauchy distribution. Furthermore, the sampling distribution of the mean of this middle portion of the data is approximately normal. As such, statistical software can serve as an important piece of helping students understand and apply key concepts in mathematics, probability, and statistics.

Cauchy distribution, trimmed means.