Will non-research but relevant extracurricular help me get into graduate school?

[RandomPersonBlowsUp]

I understand that joining a sports team or student council won’t matter at all for graduate school. However, what about internships in industry, competing in science/engineering competitions, or being a tutor that teaches high school kids math and science?

Additionally, what if you’re given an engineering internship, but it isn’t directly related to your desired research? For example, I’m interested in doing machine learning in graduate school, but I get an internship where I get to help in the development process of making apps from a relatively unknown company?

And also, I’m trying to aim for a top 25 research university, should I just maximize my time by just doing research? If I were to spend lots of time for an engineering competition, but I only reach the semi-finals, would that be a waste of time? Should I still add that to my application?

Sorry if I ask lots of questions. I tried searching all over the Internet, and I can't really find any answers. Thanks.

[TakeruK]

It's hard to find answers on this because there aren't any general answers that would be true for all situations. A large part of the grad admissions process is highly dependent on the specific people on each admissions committee and the specific needs that department has for that particular year. So, you can only get the exact answers you want if you could somehow ask the members of your specific admissions committee(s) in the week they make the decision. Of course, this is not practical (nor even possible, because the decision is often made much later than the due date). 

But if you think about what general traits that professors look for when deciding on future graduate students, this could help answer the themes in your question. I believe that faculty members look traits or details in an applicant that demonstrate that they would have a high chance of excelling in the graduate program and produce quality research while enrolled. This is weighted with which subfield(s) the department happens to be looking for that year, which is something completely out of your control. 

So, yes, all of the things you mention could play a role. Participating in and doing well in a competition shows that you have drive, ambition, talent, etc. Internships in industry can demonstrate ability to work with others, and general work experience is nice too. Tutoring can show that you are passionate about teaching and care enough about your area of study that you continue work on it even outside of the your studies. 

But it really depends on how you present these experiences. And, usually with these types of things, more isn't necessarily better. Winning one or two competitions isn't much different than winning five. Tutoring for 3 years is pretty much the same as tutoring for one. 

However, which things are going to specifically excite the members of a specific committee are going to be unknown to you. So, it's not really possible to know exactly how to optimize/maximize your time. Also, optimizing for one school may hurt you in another school.

Instead, just do what you want to do. If you don't have direct research experience and an opportunity comes up, I'd say it makes a lot of sense to choose to do that over the other things you list. But if you really want to do that internship making apps? Do it. If you want to tutor on the side, do it. If you want to enter that robotics competition? Do it. Applying to grad school is not spending years of your life in college maximizing every aspect of your life to get in. Instead, it is reflecting on your college or other past experience and highlighting the parts that make you a good grad student.

Ultimately, you are more than just whether you get into grad school, so pursue your interests where you can. There's no magic formula to get in, and trying to stick to this might just make you miserable instead. Plus, following your passions and being happy can make you more successful and productive in other aspects of your work, and demonstrating passion about things, even things outside of your field, makes you interesting.