Statistics 101. When you have samples you throw away the highest and lowest member, to counteract some random occurrence. The mean net worth of the patrons in any restaurant carlos slim frequents rises substantially when he is there.
Yes, because that is how mean net worth is defined. I don't see specifically what that argues against, except that mean is not the best indicator to use in all situations; perhaps a different indicator is appropriate, such as the income per patron by percentile. 100th percentile will be Carlos Slim, but 99th percentile and lower will be other patrons.
If Carlos Slim actually does frequent the casino, then his attendance is an important part of understanding the situation.
That, and the fact that outliers can often be discounted due to measurement/instrumentation error.
Moreover, the fact that Carlos entered your restaurant may be a significant event depending on the analysis that you're attempting to do. So you need to have to have a good rationale for dropping outliers, and you should probably also watch for bias when dropping outliers that don't support your hypothesis!
