What is statistics?
Statistics is a set of techniques, philosophically linked to the concept of probability, designed to extract summary information from data (both quantitative and qualitative data) via quantitative analysis for the purpose of improving decision-making. Economic statistics is the specific deployment of statistical methods to answer questions relevant to economic problems.
Descriptive statistics is a set of techniques for organizing data into a form that can be easily represented---metaphorically---to convey information. A batting average is a form of descriptive statistic.
Inferential statistics is a set of techniques for extracting summary information from data in such a way as to allow conclusions to be drawn from that data. These conclusions can be compared based upon relative probability of accuracy.