I'd like to give you a few theoretical examples of how you can use some of the statistical functions available in Adhoc:
The correlation function could be used for testing a hypothesis such as "Does an increased time on page linearly translate into increased revenue".
To test this, your metric X would be 'Avg. time on page' and metric Y would be 'Revenue' (let's assume for the moment that you've set the relevant variables in your implementation). The result can be inspected to see whether your hypothesis is correct and the required actions can be taken. (In this case, if increased time on page does translate into increased revenue, you could take actions to improve user engagement on your site).
Generally, a correl > 0.8 indicates fairly strong correlation
Median of a metric returns the value at mid point of the distribution. It is useful in scenarios where the average gets skewed due to outliers. To give you an example, consider that most users spend about 2 minutes on your site. A couple of them end up spending about 8 minutes on your site (perhaps they move away from their computer for a while). The presence of such data would skew the calculation of your average and would give you an inflated idea of the time being spent on your site. Median value on the other hand would give you a better idea of user behaviour on your site.
Generally its a good idea to compare the median and mean of two distributions to observe if they are vastly different and if so, to inspect the causes.
Returns the k-th percentile of values for a metric. You can use this function to establish a threshold of acceptance. For example, you can decide to examine dimension elements who score above the 90th percentile.
I've tried to give you an broad idea of how these calculations can be used. If you have any specific use cases, please let us know.