A frequent problem in statistics is deciding if two or more
of data come from the same or different populations
Perhaps the context is trying to decide if a particular medical treatment
is effective, or if a change to some industrial process has reduced the
production of pollution, or maybe even if a change in teaching methodology has
led to improved student performance? In each of these cases, you would need
any change between before and after
measurements, and see if there has been a significant change in outcome.
This is not always easy because of inherent randomness and errors in measurement.
This is called noise.
The techniques of Exploratory Data Analysis are
designed to bring out the important characteristics of data, prior to resorting
to in-depth quantitative analysis and modelling.