Statistics helps us make sense of large groups of numbers. If I give you a list of 5 numbers, you can keep them all in your head and you don't need a bunch of numbers that describe those numbers. If I were to give you the range, 1st quartile, median, 3rd quartile, min, max and any outliers, you would have more numbers to keep in your head than just the original 5.
But let's say I give you a list of 1000 numbers. You can't keep them all in your head, and you certainly don't have a meaningful way of comparing them to a different list of 1000 numbers. So here enters statistics. Now you have a language for comparing them. Do they have the same middle value, or "median"? Do they have the same maximum and minimum, or are they equally spread out (range, or standard deviation)? If the numbers represent incomes of 1000 people for two different years, and I asked you to tell me how much incomes went up or went down, statistics gives you a way of answering that question.
We teach statistics so that you can have a way of describing and comparing large sets of numbers.
Mathematics is the study of abstract concepts. Mathematics is the language of abstraction. The numbers 1, 2 and 3 are abstract concepts. There are studies done on crows that found that crows could count to 3 and also keep track of odd and even. So if 5 people went into a building and 3 people came out, the crow would think that the building was empty. It's common in some aboriginal tribal languages that numbers are 1, 2, 3 and many (or sometimes just 1, 2, many). that indicate a limit to abstraction even of counting, among the native speakers of that language. But once you have a limitless set of numbers (and limitless is itself an abstract concept), what can you do with them? You can add, subtract, multiply and divide them. These are abstractions. You can assign a letter to represent an unknown quantity, but there's so much more that you can do with that. You can have one unknown quantity be based on some set of arithmetical operations of another unknown quantity. Even just sticking with the abstraction of just numbers, we might want to come up with a way to describe a number that's between two whole numbers (e.g. fractions or decimals), and then try to figure out the rules for how fractions and decimals work.
Math is the study of abstraction.
Statistics is the study of large sets of numbers.
