All statistics is based on mathematics. Statisticas is all about summarising information - which may or may not be numerical - using appropriate mathematical techniques.
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They are running businesses, so that can involve a lot of mathematics. The skills needed to cut hair, and even things like how much materials to use, how long to leave hair when cutting and so on, all involve mathematics.
The word "involve" is very broad so that one could always find a way to relate anything to mathematics. We can prove this as follows. Suppose you found one thing that did not involve mathematics. You have used the word "one" in that description, so you have involved a number (i.e., a mathematical object) in the process.
Mathematics is a useful objective means of describing many physical issues.
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John Napier was famous for his work with logarithms.