When we were in high school , we studied statistics along with mathematics. And as per Wikipedia " Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation". Please see the following link.
Statistics was historically separate from mathematics. Probability has always been considered as a branch of mathematics although it had low prestigue until Kolmogorov gave probability theory a rigouros foundation in 1933. Probabilistic models have played a more and more prominent role in statistic, but there are still practical aspects of statistics that have little to do with mathematics.
if you change some names, a random variable to measurable function, etc. you will find that probability theory is more or less measure theory on measure spaces with finite measure. Statistics arose as applied probability theory to develop estimators and decision processes to apply. So is statistics a mathematical topic is a complex question. In many universities - statistics is a separate department. It may actually be in the engineering school when the mathematics department is in the school of science. I look at statistics as an applied probability. But at the end of the day what does it really matter how you compartmentalize it?
If one want to say something about a population based on a sample one may use probability theory, but in statistics one often find the numbers for the whole population rather than the numbers in a sample.
For instance, how many live in Germany compared with France? Should one compare citizens or should one count persons that have an official address in those countries? The answer has little to do with probability theory, but it has a lot to do with counting in the most relevant way.
I think statistics is part of applied mathematics. Applied mathematics differs from pure mathematics in that it emphasizes using mathematics. Statistics is used social sciences and business as well as agriculture, physical sciences, and computer science.