Jump to content

Type II -- Population Trends in China


Karl H T

Recommended Posts

how can you describe "how well your model fits" the data? is it enough to say all the points lie near the the model?

I have no experience with type II IA's yet but if I were to do this task, for that part I would say something like: the data points fit the curve well even though point (X, Y) does not fit the curve that well and the curve should plateau off at the end. Something like that, really. Just like describing graphs in Science :austin: And yes as gldurocher said, don't forget to plot the function and the data set on the same set of axes :panic:

  • Like 1
Link to post
Share on other sites

How do I go about starting a type 2 IA like this? Should I just jump right in with the first question about the relevant variables and parameters, or should I find some background information about the population in China during this 58 year period?

When it says analytically develop one method, should I do all the calculations for finding the regression I preformed on my graphing calculator, or say I used technology to find a model that fits the data?

IB is a new program in my school, and I'm a part of the first IB class, so my teachers are just as clueless as me.

Link to post
Share on other sites

How do I go about starting a type 2 IA like this? Should I just jump right in with the first question about the relevant variables and parameters, or should I find some background information about the population in China during this 58 year period?

When it says analytically develop one method, should I do all the calculations for finding the regression I preformed on my graphing calculator, or say I used technology to find a model that fits the data?

IB is a new program in my school, and I'm a part of the first IB class, so my teachers are just as clueless as me.

You need to have an introduction before you jump into any of the stuff that the portfolio asks you to do, and that us where you can put the background information about regression analysis and what not.

Try a program such as advanced grapher, it only works for windows computer but it is an excellent tool, and put pictures into your portfolio to show that you used technology. The pictures prove you used technology and you can then reference them and say stuff like based off of the graph etc.

I hope this helps, if you have any more questions you can ask me! IB has been around my area and school for a long time so we all know the drill. ;)

how can you describe "how well your model fits" the data? is it enough to say all the points lie near the the model?

for that section i would think that you just plot both sets of data on the same graph. yes, no?

i think my math teacher said something about an R value that is a systematic way that can actually tell you how accurate the graph is to the points.

(www.bized.ac.uk/timeweb/crunching/crunch_relate_expl.htm)

I hope this helps and the site should explain the R value better than i can :P

Link to post
Share on other sites

what are variable and parameter?

How long have you been studying math? :) I can't believe that you don't know what variables are. x and y are examples of variables. There is this formula in Physics world:

F=9*109*Q1Q2/r2

where F, Q and r are variables and 9*109 is a constant. Being a variable means that its value can be anything, depending on the domain. Let's say Q is an element of Real numbers. Thus, Q can be any real number! It may be -0.9, may be 0, may be √7, may be pi, anything.. That's why it's a variable.

Parameters..not really sure either but you may want to read this quote below v

I think Parameters can be any numbers.

I do not know if you learn this in SL, but let's say you have 3 expressions in which there are 3 variables: x, y and z.

Example:

2x+2y+z=1

3x+12y+3z=6

x+4y+z=2

Solving the above equation by doing RREF, it wil turn out that z is a parameter, z=t given that t is a real number

6y+z=3, y=(3-t)/6

3x+z=0, x=-t/3

That means, t can be anything. can be -8, 0, 1.2, 23, 94, etc... and thus the solution of the system is a straight line

If it's still unclear let me know I will explain it more clearly.

Link to post
Share on other sites

I'm analytically developing a model based on:

At3+Bt2+Ct+554.8 = P

Any help on how to solve the three constants A, B and C?

Substitute some sets of values of t and P and solve it using matrices..?

Say (t, P) are (1, 2), (2, 3) and (3,4). I am picking random constants btw.

Then you will get:

A(1)3+B(1)2+C+554.8 = 2

A+B+C=-552.8

A(2)3+B(2)2+2C+554.8 = 3

8A+4B+2C=-551.8

A(3)3+B(3)2+3C+554.8 = 4

27A+9B+3C=-550.8

So you now have:

A+B+C=-552.8

8A+4B+2C=-551.8

27A+9B+3C=-550.8

Then you can solve it with matrices. I doubt if you learn it in SL but I'll do RREF. Or you can try using substitution or elimination :)

PS: if it was a quadratic function I would find the discriminant to get some expression. idk what we can do with cubic functions though, sorry.

  • Like 1
Link to post
Share on other sites

How do I go about starting a type 2 IA like this? Should I just jump right in with the first question about the relevant variables and parameters, or should I find some background information about the population in China during this 58 year period?

When it says analytically develop one method, should I do all the calculations for finding the regression I preformed on my graphing calculator, or say I used technology to find a model that fits the data?

IB is a new program in my school, and I'm a part of the first IB class, so my teachers are just as clueless as me.

FYI you may want to read the Math Portfolio Tips..

You should start with an intro as described in that ^ thread. Describe briefly what the task is all about. If I were to do this task I'd start with introducing the data given in the task, defining variables and parameters and modelling a function after describing what I will investigate in my portfolio :)

should I find some background information about the population in China during this 58 year period?

This is a Mathematics portfolio. No you don't need that. at all.

When it says analytically develop one method, should I do all the calculations for finding the regression I preformed on my graphing calculator, or say I used technology to find a model that fits the data?

First introduce what type of function you are going to model. Let's say it's a 6th polynomial. Give the general function first, like P=ax6+bx5+cx4+dx3+ex2+fx+g

Then you find the values of a, b, c, d, e, f and g mathematically. Show ALL the calculations you perform. If you do this with your GDC, I suggest connecting it to your laptop so you can put a screenshot there in order to prove that you have used technology.

In this part, don't find the function with a graphing software yet because right after this part you'll need to do that.

And if you have any more questions you can ask ME too! Or just post in this thread so anybody can actually help you. You may ask your friends to join IBS too, or even your teacher, so they can actually get some tips/help with their IA's, okay.

Link to post
Share on other sites

what are variable and parameter?

How long have you been studying math? :) I can't believe that you don't know what variables are. x and y are examples of variables. There is this formula in Physics world:

F=9*109*Q1Q2/r2

where F, Q and r are variables and 9*109 is a constant. Being a variable means that its value can be anything, depending on the domain. Let's say Q is an element of Real numbers. Thus, Q can be any real number! It may be -0.9, may be 0, may be √7, may be pi, anything.. That's why it's a variable.

Parameters..not really sure either but you may want to read this quote below v

I think Parameters can be any numbers.

I do not know if you learn this in SL, but let's say you have 3 expressions in which there are 3 variables: x, y and z.

Example:

2x+2y+z=1

3x+12y+3z=6

x+4y+z=2

Solving the above equation by doing RREF, it wil turn out that z is a parameter, z=t given that t is a real number

6y+z=3, y=(3-t)/6

3x+z=0, x=-t/3

That means, t can be anything. can be -8, 0, 1.2, 23, 94, etc... and thus the solution of the system is a straight line

If it's still unclear let me know I will explain it more clearly.

then, population and year are variables?

Link to post
Share on other sites

so, we can choose anything to represent it? other than P and t?

thank you for your help! but i still dont get what parameter is T_T

Well you can. but it is more logical to use P and t because they stand for population and time respectively :P and anyway on the task paper they put P(t)=function, right? so yeah..

Sorry I can't help much with parameter either :) don't really understand it. I suggest reading http://mathworld.wolfram.com/Parameter.html btw

Link to post
Share on other sites

Can anyone explain to me analytically develop a logarithmic function? My teacher taught us about every other function, but not this one. Thanks so much!

I think I explained this somewhere in this thread or in another IA thread but anyways..

Define the general function. May be y=a+b*ln(x) or even y=a+b*ln(cx+d) but may be harder

Then if you choose the first function, substitute 2 sets of values of x and y that you get from the task, which are t and P respectively to find a and b. You will get 2 expressions in terms of a and b which you can solve mathematically.

If you choose the second function, substitute 4 sets of values of x and y that you get from the task, which are t and P respectively to find a, b, c and d. You will get 4 expressions in terms of a, b, c and d which you can solve mathematically also.

Anything else just ask again :gluck:

  • Like 1
Link to post
Share on other sites

do you guys graph the year on y-axis and the population on x-axis? or the other way round? because i graphed the year on the x-axis but the result seems like a straight line and when i did it the other way round, i got a curvy line. please help!

I've figured out what type of function I want to use, but I'm experiencing some extreme difficulties with "analytically" finding the values of a,b, and c in a cubic function. Any ideas on how I could find these values?

How do you decide which one to use? do you explain what functions you are going to use first on the paper? then finally you decide? is it logistic?

Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...