Although they are closely related, there are various differences that set mathematics apart from statistics. In various academic institutions, statistics is usually provided as a form of applied mathematics. One of the key differences between the two disciplines concerns how problems are solved. In mathematics, structured approaches to problem solving are applied (“What the Difference”, n.d). The structure of these approaches involves such tools as theorems and proofs. On the other hand, statistics largely relies on intuition for problem solving. This is not to say that guesses are the fundamental foundation of problem solving in statistics. Instead, it means that one combines their intuition with established concepts to solve problems. Another difference regards the universality of laws. On the one hand, mathematics employs laws that are applied universally (“What the Difference”, n.d). For example, mathematics has developed models which are employed in situations that are similar. On the other hand, statistics lacks universal models and procedures for addressing particular questions. Essentially, statistics allows for the development of unique approaches to given questions. Statistics has some room for personal judgment whereas mathematics requires strict adherence to established protocols and models.
Mathematics and statistics differ in their approach to solving real-world problems. Using idealized models, mathematics assumes clarity and a deterministic nature of problems in the world. (“What the Difference”, n.d) Statistics is more realistic in its approach to the problems. As opposed to mathematics which relies on idealized models, statistics acknowledges the randomness of events and attempt to develop solutions which account for this randomness. Another key difference between these disciplines regards the perfect environment that facilitates their application. For mathematics to be applied beautifully, logical rules that can be expressed in the form of equations are required (“What the Difference”, n.d). This is not the case for statistics. This discipline is most appropriate in situations with uncertainty. Overall, while they are largely similar, mathematics and statistics are two independent fields which share some principles but different in how they approach issues in the real world.
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Deductive Thinking
Deductive reasoning is one of the foundational concepts in statistics. Essentially, deductive thinking is concerned with applying generalizations to specific situations. When thinking deductively, one applies assumptions and premises that are known to be true for the general case to a specific situation (Suppes, 2012). If the specific situation satisfies the premises of the general case, it is established that the conclusion about the general case holds true for the specific situation. For example, consider the following construction. All American presidents have been male. Hillary Clinton is female. Thus, Hillary Clinton has never served as American president. This example uses the truth about the general history of American leadership to make a conclusion about Hillary Clinton’s political service.
Inductive Thinking
Inductive reasoning is starkly different from deductive reasoning. As noted above, deductive thinking begins with general premises and seeks to arrive at conclusions about specific situations. Inductive thinking adopts the opposite approach. It uses observations about specific situations to develop conclusions about the general case (Suppes, 2012). For example, one might say that in their entire experience, he has met African migrants who entered the US through the lottery system. He then concludes that all African migrants move to the US thanks to the lottery program. This example captures the essence of inductive thinking. As this example reveals, not all conclusions that are arrived at through inductive thinking are accurate. Therefore, before accepting these conclusions, individuals should ensure their validity and accuracy.
Applications of Statistics
The applications of statistics are as numerous as they are varied. Actuarial science, biostatistics, chemometrics, econometrics and psychometrics are some of the fields that employ statistical concepts and models (“List of Fields”, n.d). There are various applications of statistics that I feel will be relevant to my major. I am taking a program in applied statistics. Business analytics, demography and operations research are three of the most important and relevant applications of statistics. I expect that as I undertake my major, I will be required to analyze business operations. Furthermore, I understand that my major involves an examination of population dynamics, hence the application of demographics. Operations research will also be an integral component of my major. I know that my major involves the examination of complex processes. Operations research will enhance my capacity to understand and solve these complex issues. Overall, various statistical concepts and applications underlie my major.
Examples of Government Statistics
The government is among the bodies that have adopted statistics extensively. It is common for the US government to issue statistics on a wide range of issues. Crime data, consumer price indices and population data are among the statistics that the government issues. The crime data usually captures trends in the commission of various crimes. Consumer price indices highlight the cost of basic commodities in the country. These indices allow the public to understand such issues as the rate of inflationary and the general performance of the economy. On the other hand, population data focuses on various characteristics of different populations. For instance, the data could contain information about population size, income levels and access to such services as healthcare and education. In developing all these documents, the government relies heavily on statistical concepts and methods.
Summary and Reflection on Readings
For this assignment, a number of readings were provided. While they address different issues, all the readings underscore the critical role and the complex history of statistics. History of Statistics offers an overview of the development that statistics has undergone. This reading outlines how various scholars have made significant contributions to this field. For example, Girolamo Cardano is credited with laying the foundation for probabilistic computations using such simple tools as dice (“History of Statistics”, n.d). The main impact that this reading has had is that it has enhanced my understanding of the rich and complex history of statistics. Previously, I thought that statistics is a rather young field. Now, I recognize that this discipline is complex and has a rich heritage. List of Fields of Application of Statistics is another reading that was assigned for this assignment. As the title suggests, this reading identifies various disciplines which employ statistical concepts, insights and models. The fields range from astrostatistics, econometrics, machine learning and operations research to population ecology, quality control and statistical finance. As I engaged with this reading, I understood that statistics is widely applied. Thanks to this reading, I now understand that nearly all disciplines involve some application of statistics.
In addition to the readings discussed above, we were expected to explore What’s the Difference between Mathematics and Statistics. The issues that this reading addresses are contained in the title. This reading describes the different features that distinguish mathematics from statistics. The approaches to problem solving and the different uses of models are some of the differences between statistics and mathematics. Before exploring this reading, I thought that there were no significant differences between mathematics and statistics. Thanks to this reading, I now understand that the two fields are starkly different. The reading has also allowed me to recognize that the fields are somewhat interdependent. Mathematics adopts some statistical principles while statistics relies on mathematical concepts and functions for problem solving. The Way Statistics Works is yet another reading that we were required to consult for this assignment. Such issues as sampling, variable selection, types of research, hypothesis testing and design of research are the primary focus of this reading. The reading relates the complex interactions among the different issues. I attribute my newly-gained understanding of the depth of statistics to this reading. Overall, the various readings have enhanced the completion of this assignment while broadening my understanding of the applications of statistics.
References
History of Statistics. (n.d).
List of Fields of Application of Statistics. (n.d).
Suppes, P. (2012). Introduction to logic. North Chelmsford, MA: Courier Corporation.
What’s the difference between Mathematics and Statistics. (n.d).
