Statistics is the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and regularity on aggregates of move or less disparate elements.
(Mathematics is the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically).
Let's extend it to why statistics is even used.
We may turn data into information and information into practice using the methods provided by statistics. We owe it to ourselves as members of an information society to have a fundamental understanding of statistics. Without such knowledge, we are subject to the rule of those who would falsify facts for their personal gain or, even worse, dismiss all evidence and follow whatever seems reasonable at the time.
If you’re a layperson, it’s good to know basic statistics so that you can make sense of the data in your life. For example, how much is your utility bill, on average? How does it vary?
If you're a concerned citizen, you should be aware of certain fundamental data so you can understand the news and the happenings in your neighborhood. Is it accurate to say that immigrants bring sickness and crime? Is what 45 stated about El Paso accurate? Why are so many minority populations impoverished? Is it beneficial to approach infrastructure and education as communal resources, or would individual responsibility be preferable? The same question applies to health care. Even a fundamental understanding of statistics may transform such talks from emotional debates and gut instincts to reasoned scientific dialogue.
You deal with policies that are based on data and statistics if you work in the social sciences, such as health care administration, politics, or business. Do these laws make sense? Or perhaps they ought to be challenged or altered since they might be predicated on flawed research or, worse still, someone's instincts? Such problems can be answered with the use of statistics.
You undoubtedly need statistics to interpret data if your line of work involves it directly, such as in the hard sciences or finance. Understanding statistics would determine whether your actions, if you were in your position, were successful or unsuccessful since they may have a long-term impact on the lives of many individuals.
But, is statistics math
I argue no.
For example, would you consider economics or physics to be branches of mathematics? Why wouldn’t you? I mean, they both incorporate mathematics to explain their theories as well as predict results. But I argue that just because they USE mathematics in their practice does not entail that they ARE a branch of mathematics themselves.
Now this question leads to a much deeper question as to “What exactly is mathematics?” Is it a study of how numbers behave? Is it a language of the universe that we are discovering? The answer is vague and controversial but aside from that, we understand the general gist of mathematics when we hear the term. From a pure mathematics perspective, the mathematics done have no relation to the external world in which we live in. There is no practical application (at the moment) that pure mathematicians seek from their work. If pure mathematics, as its name suggests, embodies what is mathematics, then this would exclude fields such as physics, economics, statistics, etc. (applied mathematics)
When we use mathematics in statistics, it is used as a tool to describe something. For example, when we flip a coin, assuming that it’s a fair coin, we say that the probability of getting heads, P(Heads) = 0.5. The 0.5 value is dictated by the condition that we placed on it, which is the probability that the coin tossed will be heads when it lands. The 0.5 has no value in itself in the field of statistics unless it describes something. In addition, perhaps it would suffice to say that:
P(Heads) = half
Half is a bit odd and imprecise, wouldn’t you agree? Half of what? Half of 2? Half of a coin? Half a donut? That’s where the mathematics comes in. The use of P(Heads) = 0.5 is used as a tool of measurement and precision. In addition, when we argue that something is “likely”, it’s a bit vague and relative. What does it mean for an event to “likely” occur? 60%? 95%? That’s for a statistician to determine as opposed to a mathematician.
Thanks,
Eddie