Describe the difference between descriptive and inferential statistics. Solution Descriptive and inferential statistics are the two main branches of the science of statistics. Inferential statistics use a random sample of data taken from a population to describe and make inferences about the population. Inferential statistics are valuable when it is not convenient or possible to examine each member of an entire population. Descriptive statistics provide a concise summary of data. You can summarize data numerically or graphically..