Students often find Statistics as a subset of Maths, merged within the other topics. While some mathematicians kindly disagree with that idea, others despise it. The latter, ‘pure mathematicians’, find it too imprecise to be called maths. The former consider it an extension of Maths. The two subjects complement each other and function on similar methodologies. A strong grasp of maths can facilitate a better understanding of statistical techniques. Both subjects are introduced to children in school. However, statistics isn’t as prominent in the curriculum at most places. Maths is taught extensively and with much more fervour. Students who major in these subjects gain invaluable knowledge and lucrative career opportunities. Beyond academics, both subjects enhance the child’s cognitive and soft skills.
What is Mathematics
Maths is the study of quantities and numbers. We start learning the subject at a young age and continue to use it for the rest of our lives. It’s an absolute science with streamlined processes and end results. Mathematical concepts are used to observe and analyse patterns with a set of theorems. We begin learning the subject with counting and basic numeric operations such as addition, subtraction, etc. It gradually evolves into the study of quantity’s structure, order, space, and change. These functions form the four branches of maths: Number Theory, Algebra, Geometry, and Arithmetic. Maths degrees primarily lead to a career in Actuary, Data Science, Operation Research, Academics & Research, Economist, Financial Advisory, Artificial Intelligence, Banking and Insurance, Database Administration, etc. Key Topics in Maths: Pure Mathematics- Calculus, Algebra, Combinatorics, Logic, Topology & Geometry, Number Theory, etc. Applied Mathematics- Mathematical physics, Theory of computation, Dynamical Systems & Differential Equations, Information Theory & Signal Processing, Probability and Statistics, Operations research, Game theory, etc.
What is Statistics
Statistics studies data to reach conclusions and make predictions. Facts and figures are collected, analysed, reviewed, organized, interpreted to infer. It’s an applied science used to make sense of information by compiling it strategically. There are two types of Statistics: Descriptive and Inferential. As the name suggests, the former helps in description and presentation of data. The latter is used to extract information and make predictions over it. It also helps to generalise the results of a study to a larger population. Statistics degree primarily leads to careers in Data Analysis, Market Research, Financial Analysis, Cost Estimator, Banking & Insurance, Health and Medicine Research, Behavioural Sciences, Business Analysis, Industry & Operation Management, Academics, etc. Key Topics in Statistics: Graphical Distribution & Categories, Experimental Design, Sampling, Variables, Mean, Median, Mode, Centre Limit Theorem, Probability Models, Geometric Sequence, Linear Regression, Correlation Coefficients, Hypothesis Tests, Test of Significance, Inference, etc.
What is Statistics in Maths?
Students might wonder what is Statistical Mathematics despite the obvious differences in both subjects. This subject is an applied branch of Mathematics. Thus, it analyses data through tools of probability. This helps in translating the said data into relevant information. It isn’t restricted to a mere collection or presentation of facts and figures. Statistics in maths uses measure theory, linear algebra, stochastic, and other mathematical analysis. It’s a perfect blend of both subjects and highly sought after in the professional arena.
Connections Between Mathematics and Statistics
- Both subjects study quantities and relationships between them.
- Statistics is based on the Probability theory of Maths. Hence, most statistical models and tools are derived from mathematical models. For instance, the use of graphical presentations and formula structures.
- Both subjects apply logical reasoning, critical analysis, and quantitative procedures.
- Job prospects and roles are quite common for both subjects. For example, to study maths for Data Science, one needs to majorly focus on learning Statistics.
- Statistical methods and algorithms are similar to mathematical techniques. Hence, both subjects apply probability distributions, algebra, linear models, differential equations, regression analysis, decision theory, etc.
- By applying maths principles to study social sciences, statistics builds a bridge between mathematics and the real world.
Differences Between Maths and Statistics
- Mathematics is a pure science whereas Statistics is an applied science.
- Maths encompasses statistics within it. Thus, it has a wider scope and applicability in science and research. In contrast, statistics is practised more in social and behavioural sciences.
- While maths seeks patterns and their connections, statistics deal with amassing, analysing, and presenting data.
- Maths deals with metaphysical data whereas statistics depends upon the context of physical data.
- Maths gives precise and accurate results. Statistics provide estimated predictions. For instance, examining the quality of life in a city will give an approximate answer in statistics. However, measuring the area of a square room through maths will provide a specific answer.
- Mathematical science is deductive in nature. It follows a top-down approach to reach conclusions through established facts. Statistics make use of available data from a specific sample to derive inferences. Thus, it utilizes inductive reasoning.
- Pure maths involves complex systems and is considered much more rigorous than Statistics.
- Maths is rigid with a pre-determined structure with no room for change. Statistics is indefinite in its functions as it deals with real-life dynamic data. Thus, it is prone to manipulations. Statisticians need to modify their variables and measurement tools, according to each problem. For instance, The “best fit” function makes one variable preferable over the other.
- Conclusions are absolute in Maths. Statistical predictions are uncertain and vary with context. For example, a p-value below 0.5 is considered statistically significant. However, considering 0.51 insignificant depends on the judgement of the statistician and context, rather than rule of law.
- Extraneous and confounding variables can disrupt statistical conclusions. Such errors are already resolved in mathematical formulas and don’t affect results. For example, gender bias can affect a statistical study of privilege among people.
Maths and Statistics differ in their functions of measurement, context, and variability. Despite their differences, these interrelated subjects are extremely crucial in the modern world. While Maths is essential in academic structure, Statistics is highly relevant in daily life and employment opportunities. Especially with the rise of a data-driven lifestyle. As the world edges towards technology and digitisation, both the subjects proffer promising careers. Quit debating maths vs statistics, as there are no winners or losers. Both of them are equally significant in their own manner.