Question

discuss any advantages of a graph showing a whole set of data has over a single measure, such as an average

Answer 1

With a graph, you get several qualitative measures that utilize the human eye, as the premier visual analysis tool we have, can lead us to ask more quantitative questions. For example, it will quickly pick out outliers. It can also help suggest trends or changes in variance over some values versus other values. It can easily detect clusters or groups of data that might indicate multi-modal effects. It can even suggest whether data are linear, quadratic, etc. This is far more that an average could provide alone.