Kindly I don’t understand what is the goal of finding the Most Extreme
The general purpose of clustering is to try to identify patterns in data by separating the individuals into groups. In this lesson we separated the senate into two groups, based on votes cast, and found that those groups closely align with the party identity. Finding the most extreme individuals here tells us which Senators are the “most Republican” or “most Democrat”.
In another example, if we tried to separate a dataframe of cars into groups based on input like weight, mpg, 0-60 time, carrying capacity and emissions ratings, the groups would probably be something like “eco-friendly” and “utility”, and “sports car”. Finding the extremes would tell you which car is the best representitive of that group.
Perhaps you have a data frame of customer purchase histories that you could cluster in a way that showed potential fraudulent activity. Finding the most extreme would be a good place to start your investigations.