Statistical graphs are one of the most important tools of a data scientist. Typically every single data analysis begins with explorative data analysis (EDA) which is basically visualizing the data. This step tries to identify clear relationships in the data, abnormalities - e.g. outlier - and helps to generate hypothesis.
Of course this is not the only application of statistical graphs. Perhaps even more importantly graphs are used as a tool to present and explain results. A scientific graph often says more than a thousand words.