The Difference between Math and Stats | Nathan Dalaklis

How are Math and Stats different? The relationship between the axiomatic logic of mathematics and the experimental nature of statistics and statistical methods makes the distinction clear, but stats is often lumped in with mathematics. So when should math be used and when is math not enough and stats would help out more? In this video, I go through some of these differences in order to explain the nature of statistics, a subject that has always thrown me off guard in my mathematical pursuits.

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#CHALK #Statistics #Math

[axisepsilon]

Currently an undergrad majoring in CS and stat. Sometimes, I wish I could have double-majored in CS and math instead. But if I did that I would have regretted not majoring in stat.

For math, I really like the abstract and axiomatic way of approaching the problem. I think this might be the reason why I did really well in discrete math but did just okay in calculus 3 which was just a plug and chug class (It got so dry and boring that I eventually had to drop it last semester and then took it again this semester which I did pass in the end). I also took a probability course this semester and really enjoyed it. I'm taking an abstract linear algebra class this summer and really excited to learn more abstract/ pure math(Currently self-studying it and enjoying it a lot).

For stat, I really enjoy the real-world application and having more tools under my belt that will come in handy in the future (ie. machine learning, data science, etc). The fact that you can interpret real-world data and then even be able to predict/infer is super cool.

I feel like Statistics is more of a science than mathematics. It is very misleading to say that statistics is a subset of mathematics. For example, physics, one of the most math-heavy science, is generally perceived as a science even though without a deeper understanding of math, it is impossible to understand physics. The same goes for statistics. Without a deeper understanding of analysis and measure theory, one can only have a surface-level understanding of physics. This is a stage where I am right now. I only vaguely understand Random Variables and only know how to apply them. However, this does not mean statistics is math just the same way that physics is not math. Statistics from what my professor told me is a relatively new field. So there is still a lot of research going on, and sometimes what counts as statistics nowadays can be vague with the rise of data science and machine learning.

[juliacampfield]

The teacher friend is VERY happy with this video! And very excited to share with her students!

[HubertMarekD]

Actually as a „mathematical statistics” student I can say that although statistics start from the sample and real world setting motivations, the higher the level the more mathematical statistics is. For example time series could be done only studying Hilbert spaces and interpreted as a subfield of functional analysis. Sometimes statistical motivation (or maybe just call it statistics) give rise to a new mathematical objects to study etc.

[XavierMacX]

Great video. I would add that statistics can diverge further into both theoretical and applied stats, wherein the theoretical stats is kind of a hybrid field consisting in one part of being focused on data, sampling, programming, estimation, and machine learning, and the other part focused on probability theory, real/complex analysis, inference, and measure theory. Applied stats tends to feature minimal probability and analysis with a heavier emphasis on programming, ML, and subject specialization (i.e., biostats, spatial stats [GIS], survival analysis/engineering, etc.). As a former undergrad math major completing a masters in stats, I like the combination of being able to practice analysis proofs in one class while coding a program that can output point estimators in another. Heck, I know some statisticians who work ONLY alongside pure math people in the field of number theory analyzing data on the prime numbers. There is a thought that with quantum computing (if/when that becomes viable) we will solve some of the big conjectures in number theory, which could lead to further advancements in engineering and physics. Sorry for the long comment. Cheers.

[Peter_]

I have a course that is called "Mathematical Statistics" that involves a lot of integrals and things like that.
Wouldn't that be a type of math course?

[lizaburk]

Appreciate this explanation. Thank you Nathan

[tommyhuffman]

As a math lover working on a degree in Data Science, I 100% agree. Stats is often very dependent on how you look at or frame the data. I prefer Calculus for sure.

[lorenzoplaserrano]

calculus and linear algebra would be examples of maths used in stats for general calculations and probability

[ravivaradhan]

One way to think about (of course, not perfect!) is that doing mathematics is essentially a deductive process, where we go from the general to the particular. Statistical learning on the other hand is an inductive process, where we attempt to go from the particulars to the general.

[BlackopsUSN]

Bro I a freshman in college majored in engineering and switch to health so I have to take calculus in engineering but since I switch I now have to take statistics so which is harder and I am bad at math

[siddhantkohli]

As an analytics student i can real just wonder how maths and stats have changed the world n will do in upcoming years

[joelrodriguez]

The way I see it, Mathematics is about absolutes, by that I mean absolute Truth.
For example, 2+2 = 4 the Proof of that is the impossibility of the contrary.


Statistics, in my opinion, does not deal with absolutes, that is why, I know that when my answer is 1 or 0 I am wrong, because statistics does not deal with Truths statements like Mathematics does.

[austinb]

Cool vid. I’m fucking tripping balls bc idk if my college degree is worth it or not bc it’s not stem

[khalidQureshi]

Statistics is a science and not a branch of Math. Previously we have added math in computers to solve many issues which are not based on the experiences but now the world is AI and Statistical modesl are going to solve issues which cannot be solved without working on the previous data.

[yydd]

Ain't stats maths?
Why complicate this?

Stats has numbers, they have formulas, they have a method to find something. Read somewhere stats is applied mathematics. But stats is considered both art and science and maths is considered science Only that's a only problem maybe.

[NoahAvery]

If there’s a 10% chance of failure and you do it 50 times, there’s a 99.5% chance you’ll fail at some point. Does anyone know what the formula is to calculate this?

[Thefare]

Math is a branch of philosophy and statistics is a branch of mathematics. Everything that we do in statistics is mathematically defined and therefore belongs to the realm of mathematics. Give me one example from statistical theory without a mathematical definition then we can talk about math vs statistics. And you are wrong when you say the deeper you study statistics the more math comes into the design. This is the order: basic real analysis ->measure theory -> probability theory -> statistics.

[saberspeed]

Definitely feel like I like stats more than math.

[hbrpaulo]

Math is superior. I'm a statistician.