The JMP documentation is a little unclear--it just cites a book: [Robust Regression and Outlier Detection](http://onlinelibrary.wiley.com/store/10.1002/0471725382.fmatter/asset/fmatter.pdf;jsessionid=7204D63F7137C4451DBA0E5DDE27957E.f01t03?v=1&t=hzwv3tih&s=1692dd874510430e9b3f147922d941a2220ae774). 

However, it looks like the bracket contains the "highest density interval", or "highest probability density" interval. This is the smallest (i.e., shortest) interval that contains 50% of the data points. 

Suppose your data looks like this
    

> -30, -20, -10, 1, 2, 3, 4, 5, 6, 10, 20, 30. 

The 50% densest region runs from 1 to 6 because it contains half the data (six of the twelve points) and is the shortest interval that does so: it's five units long, while the next closest interval (2 to 10) is eight units long instead. 

The highest probability interval often shows up in [Bayesian settings](http://www.statsblogs.com/2013/07/20/decisions-from-posterior-distributions-tail-probability-or-highest-density-interval/), sometimes as an alternative to confidence intervals. Here, they probably mean for you to use it a heuristic for detecting outliers.