Those who have even the slightest idea about subjects of mathematics and statistics will readily agree that they are quite similar to one another. To them the linking fact between these two subjects is perhaps the extensive calculations involved in them.
Due to the usual curriculums in most educational institutions, statistics is taken as a mathematical subject by most students. However, statistics and mathematics are subjects of independent foundations. Yet, inter-relation between them is so deep that apparently they may seem as different aspects of one subject. But what is this deep relation between them that is so strong?
To understand that you must first understand each of the two subjects individually and find out the difference between them that makes them independent. Only then can you clearly see how they are inter-connected.
Mathematics
Since, you all are familiar with mathematics more than any other subject it will be wise to begin with it.
- How it is usually seen –
Mathematics is taught to all since the beginning of their primary education. It starts, by learning to count, then adding, subtracting, multiplying, and dividing and so on.
As you grow, you are introduced to more and more critical as well as complicated parts of maths. Needless to say, that this journey from simple counting to complex analysis, theorems, calculus, etc. is not an easy one. A student of mathematics or science will know this well.
Because, of this rigorous learning and traditional teachings maths is often seen as nothing more than a body of vast calculations.But is it just that? Never! The underlying beauty of mathematics is often missed by students and hence they cannot appreciate it.
- Hidden meaning –
So, what is this hidden beauty of mathematics that you cannot see? The first question that comes in this regard is that what is Mathematics? Is it a subject of science, like literature, history, physics, chemistry, etc. or something else? Expert mathematician say math’s is not a science subject. It is actually a language, somewhat like English, Spanish or Japanese. It is a language of logic. This language has extensive usage of symbols and numbers quite like in programming languages. It also has its own grammar which is a set of rules for several operations and their definitions.
It can now be a hard concept to grasp for you as Mathematics is now popular as a science subject. But, remember once degrees of Arts were awarded to mathematicians as mathematics was initially considered as an arts subject.
You know that we use languages as a basis to express our thoughts. Other subjects like literature, history, etc. are also expressed through one language or the other. Similarly, mathematics is regarded as the language of science. Science subjects like physics, chemistry, biology, economics, finance, etc. employ mathematics as a language to express their thoughts and ideas.It becomes a lot simple and compact to express theories of science through maths compared to using just words for them.
Of course, each subject that uses it moulds mathematics in their own ways, as necessary. Hence, a lot of extra assumptions and approximations are imposed on the known maths. This molded mathematics is often termed as ‘Applied Mathematics’. However, mathematicians’ ego says firmly, ‘Mathematics is a thing in itself!’
Statistics
Statistics is a subject which is formally introduced to a student at a later stage of high school education. But, it does not at all seem a new concept to them as they have been made quite familiar with some of itin primary level maths.
- A student’s reaction –
What you remember when you hear the word statistics is perhaps lots of data in a frequency distribution table, calculating mean, median, mode, r.m.s., deviations, etc.
Average calculation has been with you since your fifth standard maths so it is easy for any student to think statistics as a part of mathematics. At least, in most institutes that is exactly how statistics is treated.
However, statistics has an independent root which lies outside mathematics and more on applied science.
- What statistics is –
Application of science is extensively dependent on experimentations andtheir results. But, experiments do not give readymade results. What it gives is raw data which may consist of huge amount of errors. In the field, such data are useless unless error is eliminated.Statistics is a subject that provides tools for minimizing these errors. For example, if there are many different results to a single experiment, then usually the mean of those data is taken.Thus statistics plays a vital role in applied science and experiments.
Rigorously speaking, whenever a subject deals with lots of systems and data and wants to put some order in those reducing errors, statistics is needed.Some explanatory examples of dealing with large numbers are seen inquantum physics, thermal physics, nuclear physics, rate of reactions, micro-biology, economics, etc. This is what statistics really is.
Some differences
After knowing the true nature of maths and statistics, it will be easy for you to distinguish between them as well as find similarity. Primarily, you can see that both statistics and maths are subjects of equal priorities with comparable range of applicability. Mathematics is regarded as a logical language which as claimed before, is ‘a thing in itself’.
However, statistics is a subject which is only useful when applied to the data management of another subject. In fact, error reduction of applied science demanded birth of statistics. This subject is often regarded as a helper to every science subject when they have a handful of erroneous data. Unlike statistics, mathematicians do not much care about how maths is applied. There are several branches of maths whose applicability is still to come.
Inter-relation
The primary and foremost relation between statistics and mathematics is that both uses similar operations and rules and involve vast calculations. Subjects of science employ techniques from both these subjects and hence they both are helpers to science in some way or the other. Statistics was born out of needs of applied science.
There are few streams in maths which too have been born out of pure implicational demands, like trigonometry and calculus. So they both hold an equivalent position in the eyes of all science subjects. As statistics uses mathematics as a language as any other science, mathematics too sometimes use statistics in certain cases, like numerical analysis, finding solutions to complex differential equations, etc.
It is clear now that we should not treat both mathematics and statistics are the same subject. However, we can also not keep them too much apart because of such inter-relations. When it comes to applied science, statistics and maths is hard to distinguish properly.
In fact, often students face maths homework resembling statistics and vice-versa. But, they have to be managed accordingly. In fact, management based homework oftencontain such intermingled questions of math’s and stats, set deliberately to test management skills. In such cases, knowing the difference and the relations between these two subjects is one of the ‘Top 5 things to make your management based homework interesting’. Once you get interest there, you can miraculously tackle them.There are various professional websites which can give a closer insight to understand the difference and help you to gather more knowledge.
