When presented with a dataset, it is beneficial to identify any relationships or trends. One way in which we can accomplish this is through the application of cluster analysis, a method for developing taxonomies within a set of observations. While this technique is beneficial in marketing, research, or any profession requiring data analysis, there are many algorithms for dfining clusters in a dataset. As a result, we raise the question, which clustering algorithm is the best in various scenarios?

The Central Limit Theorem (CLT) states that the distribution of the sample mean of independent and identically distributed random variables converges to the normal distribution as the sample size increases. A common rule of thumb is to consider sample sizes greater than 30 as "large enough" samples to use the CLT as an approximation. However, the "large enough" depends on how non-normal the individual observations are distributed.