When we say word statistics, it is important to understand that there are different meanings of the word statistics. There is mathematics and part of 'higher' mathematics is mathematical statistics, sometime known as Probability or Probability and Statistics. At a university, this would be taught as an upper division mathematics followed by more advanced graduate classes in mathematics, all of which requires a mature understanding of basic mathematics such as Calculus.
A better question is, "What is the difference between probability and statistics?"
The answer is that in probability, we assume the population is unknown and make inferences about what we might see in a sample, while in statistics we assume the sample is known and use that to make inferences about something unknown regarding a population.
Working out the mean average of a sample of numbers is mathematics.
Using that number to infer something about the sample or more importantly the population from which those numbers was drawn is statistics.
Statistics describes the whole process of turning data into information and knowledge, usually but not always involving understanding uncertainty inherent in a data generating process that can be written down in terms of probabilities. Maths in this context is a useful language and set of tools that you can use to describe statistical thinking.
so,Mathematics is the practice of reasoning using known (or assumed) things.
Statistics is the practice of reasoning using data generated by unknown (or not completely known) processes.
