There are few kind of statistics: first of all - Mathematiсal statistics. This is quite a mathematical science.

Its applications widely used in many branches of science. First of all (for me) in measurement theory. When used correctly, there is no objection to this science and its methods.

The use in the so-called "social sciences", primarily in sociology, raises many questions: first and foremost - how representative is the "sample"? To what extent does the question asked by the respondent dictate the “correct” (expected) answer? And so on. Of course, this is not a statistic, but mostly a science-like hype, covering up the absence of objective methods.

There are few kind of statistics: first of all - Mathematiсal statistics. This is quite a mathematical science.

Its applications widely used in many branches of science. First of all (for me) in measurement theory. When used correctly, there is no objection to this science and its methods.

The use in the so-called "social sciences", primarily in sociology, raises many questions: first and foremost - how representative is the "sample"? To what extent does the question asked by the respondent dictate the “correct” (expected) answer? And so on. Of course, this is not a statistic, but mostly a science-like hype, covering up the absence of objective methods.

Dr. Craig politicizing mathematics and statistics. Statistics is mathematical in nature. You are trying to separate mum and daughter or father and son. This is serious.

According to the AMS (American Mathematical Society, Statistics is a mathematical sciences. See the following Subject Classification of the AMS:

62-XX

Statistics

62-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 62-01 Instructional exposition (textbooks, tutorial papers, etc.) 62-02 Research exposition (monographs, survey articles) 62-03 Historical (must also be assigned at least one classification number from Section 01) 62-04 Explicit machine computation and programs (not the theory of computation or programming) 62-06 Proceedings, conferences, collections, etc. 62-07 Data analysis 62-09 Graphical methods

62A01 Foundational and philosophical topics 62Bxx Sufficiency and information 62Cxx Decision theory [See also 90B50, 91B06; for game theory, see 91A35] 62D05 Sampling theory, sample surveys 62Exx Distribution theory [See also 60Exx] 62Fxx Parametric inference 62Gxx Nonparametric inference 62Hxx Multivariate analysis [See also 60Exx] 62Jxx Linear inference, regression 62Kxx Design of experiments [See also 05Bxx] 62Lxx Sequential methods 62Mxx Inference from stochastic processes 62Nxx Survival analysis and censored data 62Pxx Applications [See also 90-XX, 91-XX, 92-XX] 62Q05 Statistical tables.

Dear Craig Refugio, there are many statistical theorems that provide original and fundamental proofs.

Best regards

Mathematics is the "salt of the earth", and the statistic is the interpretation and analysis required for that "salt".

Both are now becomes independent branches

If a statistician does not understand mathematics he is not a good statistician and he covers his weakness through talking. Let me tell you a story: As a graduate student, years ago, I earned some money from teaching mathematics to some students of economics. Very few of them understood the real meaning of mathematics. The rest were just learning by heart the necessary material..

The main goal of statistics is to analyze mathematically the discrete or continuous data generated by some random variable (or operation) and then make a decision.

So statistics based strongly on mathematics,

regardless if some universities considered this topic as a math major or not.

Best regards

Mathematics provide us tools to analyze the numbers. Statistics use those tools to analyze events or random variables. So if any thing is using a mathematical tool will it become mathematics? We use a lot of mathematical analysis in physics, chemistry, economics, finance and others...do they purely become mathematics?..its the way it makes you feel :)

Statistics is definetly a branch of Mathematics.In many higher institutions Statistics is offered as a specialisation in Mathematics.As per my opinion mathematics, applied mathematics and Stattistics must come under same umbrella.Because all the three subjects are basically depends on mathematical concepts .

Statistics (and biostatistics) consider whether it is part of mathematics and are indispensable in research projects when testing hypotheses, because in large data series, they allow describing the results in measures of central tendency and dispersion; and even more, the results can be analyzed both parametrically and nonparametrically, to decide if they are statistically significant.

In other words, they assist in the testing of operational hypotheses to decide if the null hypothesis (Ho) or the alternative hypothesis (H1) is met

regards Jose Luis

I do not agree. Mathematics study topics such as quantity, structure, space and change. Statistics is also a part.

It's the first time I hear such absurdity.

Who ever states that statistics is not part of mathematics?

Whoever is (are), goes (go) chased by universities and research centers. Statistics is a branch of mathematics, period.

Mathematical statistics is a branch of measure theory considered a part of real analysis. It can be traced to the axioms of real numbers and is definitely real math.

However applied statistics is a totally different animal. The type of thinking in applied statistics is nowhere near that of mathematics.

If one reads Michael Loeve's wonderful book "Probability Theory" one finds that probability is measure theory theory over spaces of finite measure equal 1 with the names changed. For example a random variable is really a measurable function. The probability density function is the derivative of the measure, etc. Statistics is concerned with inferring properties of the underlying population of a "random" sample to either estimate parameters of that population or make decisions. So it that respect the same rigor applies as applies to mathematics. The issue often is in practice the underlying hypothesis are not satisfied but the results are applied irregardless. So statistics could be viewed as a set of theorems and results of a field of probability theory concerned with the analysis of random samples.

When does the application of a mathematical theory cease to be considered mathematics it any branch of mathematics.

Certainly statistics are one of the main branches of mathematics. Statistical treatments are used in different branches of mathematics, for example biomedical mathematics, ...

I agree with Issam Kaddoura that statistics based strongly on mathematics

regardless if some universities considered this topic as a math major or not.

In all the universities I have visited in USA and UK and France, mathematics is divided into pure and applied, while statistics is science depends on mathematics like physics and engineering.

Do you want to define statistics according to its axiomatic structure or according to its usage? It is a subset of measure theory and is mathematics in structure. As applied, statistics is a discipline for making decisions under uncertainity. This uncertainity is so prevalent in its character that most people consider its decision making qualities as its primary characterization. Most academics therefore consider statistics as a seperate discipline. Some separate probability theory as distinct from statistics and put it on the math side. Basically statistics has so many wide and varied usages that it deserves an identity of its own.

I agree! Although Statistics uses Mathematics in a great deal, Statistics generally looses the preciseness of pure mathematics on it.

Everything depends on the definition of statistics. This term has a very broad meaning. Mathematical Statistics is definitely an esteemed branch of mathematics with all rigor and stuff. The whole spectrum of applications is an applied mathematics, but still mathematics. It is important to see the historical aspects of statistics as well.

For the majority of people applications are treated as statistics and, on a practical level, may not look as directly connected to mathematics (just statistics:)).

In order to give an answer to this question, we have first to give an answer to the question "What is Mathematics"? According to the answer given in the later, the question of the former will follow. My personal opinion is that, since statistics relies heavily on Probabilities, an esteemed branch of Applied Mathematics, Statistics may likewise be considered a branch of Applied Math.

Dear Eman F. Mohommed ,

I think you want to turn attention to the essay:

Quoting:

It is a nice essay. But you should mention the reference:

http://www.nationalmathfestival.org/more-math/

this is better for you and the followers and no one considers it as plagiarism.

Best regards

I think that Statistics is a branch of Mathematics. It walks alone but it cannot deny its great mother.

I do agree, partially. Mathematical Statistics is like a branch of Mathematics. Better to say, Statistics is one of the branch of Applied Mathematics, I guess.

Mathematics is the universal domain for all sciences, knowledge or philosophy whether that is about the statistics or not, it does not matter, I think.

I have followed this network of questions and answers. The answers are more in the sense that statistics are a branch of mathematics, with which I totally agree, as I mentioned in this network from the beginning.

We can think that Statistics and its application in living beings Biostatistics, be independent of mathematics. Both in the scientific method and in the design of research and description with analysis of results, mathematics comes into play.

If you want to be more purist, you can say that Statistics (and Biostatistics) with branch of Applied Mathematics.

Deeper thinking lies a PARADOX / DUALITY .

https://www.researchgate.net/project/INTER-DISCIPLINARY-RESEARCH-AND-ACADEMIC-ITEMS-A-PROJECT/update/5d850b3fcfe4a7968dcd74b2?_iepl%5BviewId%5D=Esey35kWT34nw06ovh4zEO71&_iepl%5Bcontexts%5D%5B0%5D=projectUpdatesLog&_iepl%5BinteractionType%5D=projectUpdateDetailClickThrough

The latest revision of the Mathematics Subject Classification (MSC) has been published a few months ago, and searchable versions are available at the zbMATH site and the MathSciNet site:

https:// zbmath.org/classification/

https://mathscinet.ams.org/mathscinet/searchMSC .html

Mathematical statistics is a branch of measure theory. It is mathematics. However the use of statistics is totally different from app;ied mathematics. It is an entirely different philosophy. The questions, usage, intuition, and environment are so different from mathematics that it deserves its own entity. It is separate.

Mathematical statistics can be considered as applied mathematics. Almost all mathematical models are a combination of theory and data analysis. The theoretical part needs general theorems, lemmas, corollaries, remarks, and general proofs. The given observed data ( qualitative, quantitative, etc.) need to be analyzed according to the general theory and to study the effectiveness of the results related to the given data and to forecast the situation using probabilities and statistical measurements( mean, variance, expectations, correlations, probability density functions, curves fitting, approximations, etc.) Many of the important mathematical theories as probability, operation research, game theory, transportation, economics, Markov chains, distributions, and many more are strongly related to the statistics mathematical approach.