Although counts and averages are called statistics, the scientific field of Statistics encompasses much more. In a study (a study is a generic name meaning that we want to learn something about a topic by gathering data) there are three general steps; planning and data collection, data analysis, and data reporting. It is important to do all three well for a study to be successful. The role of a Statistician is to help during each of these steps to make sure that the study is made in such a way that it is as successful as possible.
For illustration, let's imagine our study is a pyramid that we are constructing, and our goal of the study is to be pointing towards the truth represented by a star. The three steps in our study are; C for Data Collection, A for Data Analysis, and R for Data Reporting. When all three steps are done well, our pyramid will be build so that we are in alignment with the truth and we have a clear path forward. What happens though if we do not perform each step well?
If our study lacks useful data reporting we are left with a structure that has no point. It may have a great foundation, but without the point there is no clear direction which way truth lies. A lack of useful data reporting could be an actual lack of report, or it could be that the report was not clear or it was never delivered to the appropriate people. Fortunately this can be fixed easily by correcting the problem with the report since the foundation of the study is already in place.
We are in a bit more trouble if we are missing good data analysis. While we have a good foundation from the data we collected, we do not know where our report should be focused on so that it is pointing towards the truth. Poor data analysis can range from using incorrect methods (which means we will be missing the truth) or not powerful enough analysis, through to an analysis that is too complicated for an effective report to be made. Fixing poor data analysis after the fact means that we must replace or append the report, but only after the correct data analysis has been conducted.
The most dire problem when conducting a study will come if our data is not worth building on. If we miss this piece then the analysis and the report we make (even if done as well as possible) have little hope of pointing to the truth as the foundation that it was built on is hopelessly flawed. Even worse; if our study is built on poor data we may not even notice that it is not pointing towards the truth until it is too late and decisions have been made because of the direction the report is pointing. Poor data can be things like biased samples, inappropriate collection techniques, incorrect results recorded, etc. Unfortunately if the data collection step is not good it may be easier to start a new study that is built on sturdy footing rather than prop up the current study and hope it points in the right direction.
A Statistician's role throughout a study is to assure each step is done as well as possible, and if problems arise use their expertise to make sure that the structure can be corrected in such a way that it still will be pointing to the truth.
