Is this weird?

Pre-College Topics High School Life
1

Okay, so I really love math. I eat, drink, and breath it. It’s nature, it’s expression…everything about math is beautiful - except statistics.

I’ve been self-studying upper level maths, like Algebra II. I’ve also been studying statistical math classes, like AP Statistics.

Now…here’s the problem. I find statistics completely boring and ugly. But, that’s not the catch. I’m complete crap at it. I don’t understand 7th grade probability questions and I’m doing math two grade levels ahead of me. I’m not trying to sound narcissistic.

Is this weird? I can do algebra and geometry above grade level, but not statistics. Data is similar, but easier. I don’t know. Are they different ways of thinking or something?

*By studying AP Stats, I just look over it and try to learn simple topics. I’m full blown learning Algebra II

2

Algebra and Statstics are very different (And Geometry is pretty different then both of those). Honestly, not everything is going to come easy in life, and you might just have to work harder for Statistics chapters :slight_smile: And since you’re not good at Statistics, you’re going to be very tempted to never take a statistics class and only take algebra, but DON’T do that! Frankly, learning something you already know isn’t learning, it’s sitting in a class, taking tests, and getting A+'s on all of them. You should take a statistics class as a challenge because otherwise you’ll never improve. Obviously, the only way you’ll get better at statistics is practice.

You’re pretty lucky that you are 2 years ahead and math comes easy to you. There’s always going to be something you’re not great at, you just have to practice! Most people struggle in all parts of math, so you’re pretty lucky :wink: It’s not weird at all, everyone struggles with some math! (it’s geometry for me).

3

As a math major, I also took AP Stats in HS and wasn’t a big fan of the course, even though I got a 5. Don’t get me wrong, statistics is an interesting subject, and there are some nice theorems.

I don’t know if this is correct in your case, but most high school Algebra II texts introduce basic counting techniques (permutations, combinations, some basic identities) and probability. To be honest, I would hold off “self-studying” AP Stats until you have mastered topics from HS algebra. In reality, many math majors don’t take statistics until after taking calculus and linear algebra, since the latter subjects have all sorts of applications in statistics.

If you have any other questions, feel free to reply here or PM me.

4

It’s absolutely not “weird.”

“Math” is a pretty general term. There are lots of different courses under that single umbrella. It’s only natural that you have a preference for some over others.

And, no narcissism has nothing to do with it.

5

I haven’t done any statistics (yet), but probability is definitely my weakest math topic. It just doesn’t click with me the same way that other math seems to. However, I’m planning on taking AP stats and learning some combinatorics through AoPS. I refuse to let myself hide from probability and statistics forever, because I agree that it’s good for you to struggle with it (to an extent, of course). I wouldn’t take my chances with self studying statistics unless I suddenly get a lot better at it, but I have no reason to self study it anyway.

I was so surprised when I got a simple probability problem right on a sample AMC-like test and I didn’t even resort to listing out all possibilities, haha.

6

@MITer94, I just cannot understand. When it’s talking about probability with rolling dice, or anything related to probability. I’d say I worded my original post wrong, as I’m not sure if probability falls under statistics?

Like, for example: What’s the probability that John will roll a sum of an even number on two six-side dice?

That’s not homework, so I’m not asking for help, but it makes no sense to me. It’s weird, really weird. I’m sure that I could probably understand calculus better than probability, data, statistics, what have you.

I’m the type of person that likes knowing the answer exactly, and not having to think about it too hard. Proving things in Geometry will probably be annoying.

That’s why Line of Best Fit messes me up in some cases. Linear or not. I know there is a “best” one, but it’s not really definite.

7

For starters, you may be very surprised to find that you LOVE geometric proofs! They’re like a puzzle; you have to play with the pieces until you can make them fit. Don’t discount them-- or anything you haven’t yet studied-- until you get there.

For what it’s worth, lots of very bright kids struggle with probability.

And the whole “line of best fit”- here’s why it’s a problem: You’re in, what, 7th grade?? You’re still growing and changing. The things you love today will NOT be the same things you love as a college Junior or Senior. The things that you struggle with now will come easier to you in time as your brain continues to develop and as your life includes more knowledge and experiences.

8

@IrrationalPepsi Wait, this one should be fairly straightforward. Do you not understand what the question is really asking, or why the probability is 1/2?

Honestly, I don’t know what I feel about proofs in the standard geometry course. Being able to prove statements is undoubtedly useful if you want to study math, but most HS curricula restrict proofs to only geometry, and only to proving shapes congruent/similar using a set of rules. Perhaps you could try proving theorems you’re learning in Algebra as a start.

Assuming you are referring to the least squares regression line, that is well-defined given a set of (x,y) points.

I have to agree with @bjkmom on this one; you are still quite young and probably don’t have the mathematical maturity (yes, this is a widely used phrase) to self-study AP Stats or calculus or other advanced subjects yet. In particular, don’t rush. I suggest holding off on AP Stats until after taking Algebra II and gaining a firm grasp on how to solve these probability questions as above.

9

Algebra 2 isn’t “upper level” math lol. I’m in AP Stats really boring too. But most people in my class find it pretty easy. You’re studying stats a bit easy all by yourself, which I think explains why you find it hard. Once you actually take it in HS with a proper teacher hopefully you’ll have a much easier time.

10

I’m actually in 8th grade. I’m in Algebra I/Math I. Math II is just a continuation, Math III is what I’ve been studying. Its essentially Algebra II. I consistently make high scores, highest, actually, on test and I suspect that trend to continue. But that’s extrapolating…see what I did there? See, I understand terms but I don’t understand the processes. I’d say I’m pretty weird.

That’s 1/2? I’d never get that in a million years. I’d say that I understand math very well, but I don’t mean to sound conceited. I understand what y’all are saying. I should wait a few years, but the only questions I missed were probability on last year’s math exam. (7th grade). Maybe my approach was wrong in class, or something. Any tips?

I wanted to understand it. I really do. Maybe if I could then I’d like it. Probability is what kills me…ugh. Another example: If Johnny rolls two dice, what’s the probability that one will roll an even number, and the other rule a number above 4. Like, what the heck?

I’d say I turned a minor issue into something big.

@outlooker , it’s not AP Stats that I’m struggling at. Yesterday I decided to stop looking over it. I’ve realized that 7th grade probability is what caused my problem. 8th grade Math doesn’t involve probability in NC. Math I doesn’t either…I don’t think so. We have two more units: Volume and something else.

11

It took me a few minutes but the probability is actually pretty simple for that problem you mentioned:

For the sum to be even, you need to roll either two even numbers or two odd numbers. Chances of rolling an even number is 3/6 or 1/2, and the chances of rolling an odd number is also 1/2.
So the chances of two odds is 1/2 * 1/2= 1/4
The chances of two evens is 1/2 * 1/2 = 1/4

1/4 + 1/4 = 1/2 chance of being even

At least, that was my reasoning…

ETA: I’m referring to the first one

12

As I understand it (from last year’s College Stats…), if you want the probability that 2 (independent) events will BOTH happen, you multiply their probabilities. Independent meaning that one roll doesn’t affect the next – it’s not like the die will avoid rolling a 4 if it has come up already.

For this situation, you want an even sum. When can a sum be even? If both numbers are odd (1 + 3 = 4) or if both numbers are even (2 + 2 = 4).

Taking the first case, that both numbers are odd. How many odd numbers are there on a six-sided die? 1 2 3 4 5 6 – there are three odd numbers and three even. There are 3 odd numbers out of 6 total numbers, so the probability that the number rolled will be odd is 1/2. You want both numbers to be odd, so you multiply the probability of one number being odd and the probability of the other number being odd. 1/2 * 1/2 = 1/4.

Then you do it again for both numbers being even. The same thing happens: there are 3 even numbers out of 6, so the probability of one number being even is 1/2. 1/2 * 1/2 = 1/4.

Now you have two cases. What can you do to find the OVERALL probability? Add them together. 1/4 + 1/4 = 1/2.

(More experienced statisticians, please let me know if I am wrong!!)

13

@IrrationalPepsi you seem to be making a bigger deal than it should be. If you can’t think of any other way, you could just list out all the combinations, where (x,y) corresponds to the outcome of the first die roll and second die roll.

(1,1)
(1,3), (2,2), (3,1)
(1,5), (2,4), (3,3), (4,2), (5,1)
(2,6), (3,5), (4,4), (5,3), (6,2)
(4,6), (5,5), (6,4)
(6,6)

1+3+5+5+3+1 = 18 equally likely possibilities to obtain an even number, out of 6*6 = 36 total → probability = 18/36 = 1/2.

A much faster and probably more intuitive way is to note that regardless of what the first die shows up, there is a 1/2 chance that the second die roll is so that the sum is even (this happens iff the second die roll has the same parity as the first).

Possibly, but to me, it seems the bigger issue is a lack of conceptual understanding of the topic. For example, if you are taking calculus, you shouldn’t jump straight into all the differentiation and integration rules (e.g. chain rule, product/quotient rule, integration by parts) without a fundamental understanding of what these things actually are.

Start with some simpler problems:

I flip a fair coin twice. What is the probability of seeing both heads? What about at least one head?
I flip a fair coin three times. What is the probability of seeing at least two heads?
I flip a fair coin 99 times. What is the probability of seeing at least 50 heads?

14

I agree with a lot of the other posters, Math is a really general term and you’ll probably have different feelings towards things like statistics, calculus and geometry than you have for algebra because all the topics are vastly different.

I also do some competition math and really enjoy doing math, but I couldn’t stand geometry proofs in school. I’m trying to self study AP Stats now and I just find it really confusing.

As for probability I quite enjoyed it. I know when I first started learning it, my math teacher suggested we make a 6x6 table of all the possible values for the sum or product for the two dice. Then you can visually see and count how many are even or prime or whatever and divide it by 36.

15

Okay. Thanks y’all! I’m gonna stop this here. It’s getting crazy! You guys are smart ;). I want to do something with math, possibly become a math major. I know statistics is just another subject, but whew.

Have a good day :slight_smile:

16

There’s also the whole “HS algebra” versus “algebra” that math people refer to (for example, generalizing the notion of polynomials to polynomial rings), but I won’t get into much detail here.

In short, there might be fields of math which you really enjoy, and fields which you don’t enjoy or aren’t good at, and that’s okay. But you should start with the fundamentals; as I’ve said earlier, it’s probably not a good idea to learn statistics or calculus on your own without a solid understanding of topics from HS algebra.

quote

[/quote]

@bodangles If you see my second solution, it sums down to, regardless of what the first roll is, there is a 1/2 chance the second one is the same parity.

That reminds me of some other nice problems where the solution hinges on not knowing whether A or B is true, but knowing at least one of them is true. It gives a really nice proof to the statement “there exist irrationals a and b such that a^b is rational.” (other than a = e, b = ln 2 or something :slight_smile: )

17

I’m not studying calculus yet. I’m giving up on statistics. I’m gonna try to get a basic understanding of probability before I move on. Then, I’ll try better. Is it a different way of thinking or something? That’s my last question :stuck_out_tongue:

@MITer94

18

@MITer94 That’s certainly a clearer and more streamlined way of thinking about it, haha.

19

@IrrationalPepsi Sometimes; oftentimes there might be a clever shortcut that eliminates the need to list out all the possibilities. AoPS has several resources, including entire books on counting and probability, but there are many other resources. But yes, in general, you might want to try different approaches to a problem or look for clever solutions.

Just to be completely clear, I’m not saying you should “give up on statistics” entirely - I’m simply recommending holding off until getting a solid foundation in the earlier subjects. You could also take statistics after calculus.

20

I know I’m months late, but this popped up when I searched something and felt the need to answer it. I am currently in AP Stats and it sucks. I love math too, but my stats homework is basically to read a giant paragraph and spend 20 minutes interpreting the data and drawing a complex graph. I miss actual math with calculations.