Statistics Projects for High School Students

Recent questions in High school statistics
High school statisticsAnswered question
Maribel Mcintyre Maribel Mcintyre 2022-10-31

What is 1 % of 1 billion?

High school statisticsAnswered question
Marlene Brooks Marlene Brooks 2022-10-31

Finding the function of a parabolic curve between two tangents
Alright folks, first question here so let me make the situation and background clear.
I'm attempting to start studying for aerospace engineering, so I'm working on improving on my math skills as we speak, but couldn't help "jumping in" to some of the design and starting to look at it. I'm not adverse to algebra, although my calculus legs haven't been walked on in awhile, which is why I haven't been able to get farther myself on my own question.
Another side reason is that I'm attempting to get the gist of equation-based curves in CAD, so rocket engine nozzle curves are perfect for learning that...if I can figure out the equations!
If the format or my thoughts seem a bit off, I have an idea of the concepts in play here, my math skills have just atrophied a little too much for my own comfort.
What I'm working with is the G.V.R. Rao approximation of a bell nozzle curve; essentially,
f c = { 0.382 R t For divergent throat curve f p Main body
Where f p starts from a point with a tangent of angle θ n and ends at a point with a tangent of angle θ e . f p also has to fit in a region equal to L f 0.382 R t , where L f is the complete distance between the throat and exit plane, so the displacement in the x- or y-axis, depending on how you view the rocket (orientation-wise).
I do know how to differentiate the curve f p to get f p and then find the angle of the slope at a point, but this is backsolving from two slopes to find the region in between.
If it's any help, ideally I'd be constructing the nozzle in CAD vertically, that is, y n > y e
What I'm looking for is help toward the derivation of a formula that allows me to construct a curve that is smooth between the two points. One of the reasons I've had a hard time figuring out the exact parameters is because it feels a lot like curve-fitting, which I haven't had much experience with.
If anyone can help break it down for me, it'd be much appreciated but if the question turns out to be too vague, references to places where I can get the requisite learning would be also appreciated.

High school statisticsAnswered question
Tessa Peters Tessa Peters 2022-10-30

What Are R-Modules Used For?
Kind of a simple question, but what exactly are R-modules used for? Do they have any engineering applications?
I am a graduate student researcher in computer architecture, a subfield of computer engineering. Specifically, I do research on the best way to build future general purpose processors
One thing I am looking into is if it is possible to apply mathematics to improve the design of CPUs. That is, can we use concepts from mathematics to improve the execution of general purpose programs on hardware. CPUs are a massive engineering design problem, and where exactly we could improve the design by applying math isn't entirely clear.
What I don't have is a very deep mathematical background. I have taken an introductory abstract algebra course and one in coding theory. I've also read a number of coding theory papers...
I know that other electrical engineering subfields like communications and compressed sensing have successfully applied elements of linear algebra and abstract algebra and have gotten very good results.
The fact that this particular question spans both engineering and mathematics makes it both hard to formulate and to discuss with people. I'd be happy to talk about it in more detail, but I'm not entirely sure what the best forum would be for that.
At least for now, I figured a good place to start would be to see if other people have successfully used some of the more abstract math concepts in engineering systems. One of the few I am aware of are R-modules, so I figured I'd ask if anyone knows of some engineering uses of them...

High school statisticsAnswered question
djo57bgfrqn djo57bgfrqn 2022-10-26

What I have found is that I love theoretical discussions of mathematics and proving theorems, though the education system focuses on doing exercises and applications, and that is what grades are determined on. I have a hard time doing exercises mainly because I don't find them motivating, although, I admit, doing the exercises does cultivate one's intuition to a certain degree.
Up until now my main technique of learning was to take meticulous notes from textbooks(not in class as all they do is mundane exercises), think about those concepts and then practice exercises before exams, and it worked fine for discrete math, precalculus, and even the first course of calculus, which was mainly focused on derivatives. Further. I as able to maintain A's in all my classes with enough energy left over to even do very well in other classes.
However, this hasn't gone too well in the second course of calculus, which is mostly about integrals of various functions and their applications and techniques. The instructor usually does problems on the board step by step without any discussion for what we are doing. For example, both the fundamental theorems were introduced and given about 15 minutes of time to discuss. But, of course, this could be bad teaching style.
My question is this, should I learn math theoretically and understand the material well even though on tests this would mean getting about B's that I have gotten or should I only care about the grades and just do what I am told, like a human calculator, practice exercises and just focus on getting A's? What is the better for me in the long run if I want to get into a decent grad school? And have any of you ever had to decide between getting an A or spending more energy and time actually learning the theory, which is more satisfying? I could be looking at this completely wrong and perhaps there is a way to do both? Thank you and your input will be appreciated.

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