There are many convincing articles on the importance and/or usefulness of statistics. I am writing this one, however, for explaining instead of convincing purposes. I try to rationalize the role of statistics in the modern world as you perhaps have already appreciated. My doing so takes a somewhat philosophical approach, analyzing statistics as a cognitive method, describing what statistics is in its bare essence, what it does, and in what ways it benefits us. My goal is to provide a more general and fundamental perspective, which as a topic seems quite under-explored.
My analysis starts off from a common intellectual activity: understanding. Understanding how things in this world work is in general very difficult. What we can directly do is sensing: see, hear, touch, taste, and smell, all these give physical sensations that cause cognitive signals. Such signals are not understanding, they are observations. Understanding is to obtain or create knowledge of relationship between different objects or concepts. From observations to understanding lies there a complicated yet poorly-understood mental process.
By what approaches do we understand?
There are two basic approaches. One is deduction (deductive reasoning), the other is induction (inductive reasoning). Either one has its own strength and weakness. Deduction can lead to very deep and precise understanding, but it needs a basis to start the derivation. The basis, in more familiar terminologies, is called premises or axioms. Deduction cannot do anything to the basis, which is its Achilles’ heel. In principle, understanding by deduction can be only as good as its basis, which means not that deduction cannot increase understanding, but that the outcome of deduction is determined by the basis. A good basis is often very difficult to find.
Induction draws conclusions from observations, instead of a priori basis. Often than not, conclusions by induction is somewhat shallow and imprecise. The problems facing induction are: (1) how to make/collect relevant observations, (2) how to reveal the relationship between objects or concepts from observations. Both problems are in general very difficult to solve.
(So there is NO easy approach to understanding. That plus the fact that our sensations does not directly result in understanding is why understanding is in general very difficult.)
Statistics is a tool for induction. It provides a spectrum of methodologies from collecting and sorting data, presenting data, to revealing relationships hidden in data. Despite of the broad range, what it does in essence for improving understanding is establishing a probability-based relationship between different objects or concepts. This is where the importance of statistics stems. Nowadays, it is much easier to generate a huge amount of data, thanks to the advanced information technologies, than to understand the data, and so statistics is ever more important for improving our understanding.