Data
Data is now collected on virtually everything that can be measured. While these datasets are important for modelling and simulation, they are also finding use as a source of insight and methods are available that extract meaning from data.
Forecasts
Can past data help predict the future? Sometimes it can be a good guide particularly when trends and seasonal variations are buried in the data.
Transform your data
Sometimes data isn't in the most convenient form to be useful. Some mathematical tricks can help transform data into a more convenient form. But beware the pitfalls!
Find the clusters
Data can suggest that individual items are related to other items and form a cluster. Algorithms can help find these clusters, and even tell you how many clusters there are.
What cluster does this belong to?
A related problem to finding clusters is to decide what cluster a new item that has never been seen before belongs to. This is the classificaiton problem.