IA Body Mass Index

[Ruan Chun Xian]

Lifestyle is not a limitation of the model.

They're looking for more things like limitation of acutally drawing the graph, limitation of whatever programme you used to draw the graph (or limitation of your eyes if you modeled it by hand but that would have been pretty tough). Focus on mathematical limitations rather than social implications of the topic.

[deissi]

To supplement to Hien's post, we cannot give you ready limitations; it is your task to find them. We can simply guide you in the right direction.

[Nitika]

I am confused. Can somebody please tell me how to find the BMI of a 30 yr old woman in the US?

[deissi]

I am confused. Can somebody please tell me how to find the BMI of a 30 yr old woman in the US?

The task states: "Use your model to estimate the BMI of a 30-year-old woman in the US."

Therefore, use the model you found in the previous question using technology to see what the BMI of someone 30 years old would be. You've plotted the model according to the data points that are given in the beginning of the extract, but you can extrapolate other values using the best-fit curve of your model and seeing what value of BMI it yields at age 30 (your independent variable).

[muaha]

hey guys, so i am currently working on my BMI math portfolio and its a bitch.

i dont really get the parameters nore do i know what to write for the darn variables ...

basically.... I HAVE NO IDEA!!!

and to make it worse i dont have a mac so i am busy looking for a freaking online graphing calculator that does all the **** i want it to do !!!!!!

please help if you can !!

[Lara.z]

HI...

I found data for females from another country but it is the MEAN BMI and not the MEDIAN BMI as given in the question... would this affect my mark? and do i need to look for MEDIAN BMI or can i stick with the MEAN?

Thank u!! =D

[Austin Glau]

If it is a country that is not very well known or with data that is hard to find, i don't think IB graders will spend the time looking to see if the data is correct. But if it England, France, Canada, ect. with data easily accesible, it may mark your grade down. I don't think the mean instead of median will really affect your calculations, it is just accuracy.

[PowerRanger]

you guys are f'in awesome! thank you lots!

[bLub]

Hi there,

We're doing our second maths coursework atm and I don't really know what to do... The one that most "interests" me is probably the Body Mass Index one... but, just as all of the types we can chose from, nothing makes sense to me (except for the very first sentence probably: plot the data on a graph! )

I would really appreciate any help!! Thanks in advance

ps: is any of the other types (i.e. fishing rods, crows dropoping nuts or logan's logo maybe "easier" than the bmi one?)

[Austin Glau]

I remember doing that portfolio ...

What exactly doesn't make sense to you?

EDIT:

What i found hard was the last part where you had to find BMI data, there was almost no reliable data anywhere ... I just used a different country (or I made it up, Im not sure but i got a good grade )

( 1) Using technology, plot the data points on a graph.

Define all variables used and state and parameters clearly.

Once you plot data points on the graph, state the variables (BMI and age, or whatever the variables are on the data you were given). By parameters,

I think they mean the range and domian, but they may be talking about limitations or something, ask your teacher if it is not clear.

2) What type of function models the behaviour of the graph?

Explain why you chose this function.

If you are having trouble identifing the function, try importing the data into excel, and making a chart from that. Then right click one data point and click "Add Trendline," and check the add equation checkbox (and the R^2 value if you want to check how accurate the equation is). Then, say what type of function it is from the equation (i.e. quadratic, logarithmic, linear, cubic, exponential, trigometric, ect.). And then explain why it is that way (i.e. if it was cubic, show how the behavior of the graph models a cubic function - it has three roots)

Create an equation (a model) that fits the graph.

3) On a new set of axes, draw your model function and the original graph.

Comment on any differences.

Refine your model if necessary.

Your equation should be close to excel's equation, if you have trouble creating an equation google it, of for trigometric equation see this.

4) Use technology to find another function that models the data.

On a new set of axes, draw your model function and the function you found using technology.

Comment on any differences.

Use the excel thing if you haven't already done it. For graphing, you can use TI Emulator or other graphing software.

5) Use you model to estimate the BMI of a 30-year-old woman in the US. Discuss reasonableness of your answer.

See what the data point for the 30 age is, and record the value.

6) Use the Internet to find BMI data for females from another country.

Does your model also fit this data?

If not, what changes would you need to make?

Discuss any limitations to your model.)

I don't think they check to see if your data is reliable, when i did this i had trouble finding good data. Once you find it, check it against the model. Limitations could be:

People could live longer than the age given.

People could have different living habits and therefore be fatter or skinnier

The data is not recent, ect.

hope this helped!

[Bee.talbot]

Wow, this certainly gave me a few good ideas. I thought about trying a logistics growth curve for the data, but I wasn't sure how to represent the unknowns in the mother function. Has anyone tried that kind of function?

I see that a cubic curve has a very good fit when I use my calculator to find a cubic regression, but when I'm choosing a function to model the graph manually, could I just use a simple linear regression (line of best fit), and then for the second part when I "use technology to find another function" can I then use the cubic?

It feels sort of like the easy way out, but on the other hand I can see a way to justify why the data can have a linear representation...

[sweetnsimple786]

I did a logistic for mine. I explained how to find the unknowns well enough for 3 out of 4 of them, but for the last one, I pretty much said that ___ is what the number should be around because of [insert good explanation] and then I guessed around that number til I found better fits. The guessing part lost me a couple of points. So how you should do a logistic is by plugging in data points that you're given. It's not too hard from there.

If I were to do a y=mx+b type deal, my teacher would call BS on that and give me low points. The reason is that I'm supposed to be able to do better work than that. And I hope that didn't come off as boastful. Just in Math SL, all of us [all-inclusive us] are more advanced than that. It's too simple. That's what I got from my teacher. Others might feel differently. You can ask yours. I'd suggest trying to fit a cubic to the data and then using a regression to find a better [or maybe just as good] cubic. That's what most of my class did.

[Bee.talbot]

I would like to use a logistic, because just by observing the graph it seems like a good fit, but with the model: A/1+Be^(-Akt), I'm not sure how to find A, B, and k. I know A will be the limit, but how do I find that in a graph which doesn't really seem to have a limit. That is, can BMI go on forever? Also, what are B and k, really?

[sweetnsimple786]

Isn't BMI like the weight divided by the height squared or something like that? Just think what that would mean if it could go to infinity or even a large number [more than double digits]

You're right about A. One thing I would change is what you're raising e to. Why raise it to -Akt? Why not condense the -1, the A, and the k to one value? You could either look for this new value or you could look for k and multiply -A to it, which seems like extra computation. B affects the steepness or gentleness of the curve around the inflection point [the point pretty much in the middle of the curve], I think. k is called the relative growth factor, but I've only used it when talking about population growth/decay. I used a slightly different logistic for mine where I didn't need to specify a k.

So to find the unknown constants, you can use points that you're given and plug them into your equation. It's the more complicated version of solving for the y-intercept when you're given the point (0, 1) and the equation y=2x + b. To find b [the y-intercept], you plug the point into the equation. 1=2(0) + b. 1=b.

Since you have three unknowns in the logistic, you will need to use three points. Basically, you're setting up a system of equations and solving the system.

[Bee.talbot]

Haha, oh imagine what infinite BMI would look like!!

I think I see what you're saying, but let me just be sure:

I want to find the three unknown constants A, B, and -Akt (which we'll call C, I guess). Right?

So I would set up a system of exquations using points like (0,1) (1,2) and (2,3)...

then I would use A/1+Be^C, but put in the points? So, 1 = A/1+Be^C...but where can I plug in x? I think I'm confused by the linear example...

Thank you, though, for your help!

[sweetnsimple786]

With your first logistic, the independent variable was t & your dependent was y. Since you're not using time for BMI, you won't really see t as the independent variable, but you can leave it as t if you want. It's just a letter, really. But the t would be the x. So it'd be like C=-Ak not C=-Akt [if you use t as the independent]

And yes. Just to clarify, the points you use are going to be the ones you're given, not ones you made up. I don't think you'll use made up points, but I just wanted to say that for peace of mind ahah

[Bee.talbot]

Ah, I see! That makes more sense now.

So, My unkowns are still A, B, and C(-Ak) so I could use equations like:

16.4 = A/1+Be^(2C) , 15.7 = A/1+Be^(3C), and 16.8 = A/Be^(10C)

and then solve for the unknowns. Now, I don't recall learning how to solve a system of 3 unknows without a calculator program, so would that be against the "manual" part of the question? Of course, I could be brain-farting right now and forgetting the simplest details.

Oh, I just made up points because I though it was against the rules to use the actual data points for the portfolio, as it would be "giving answers" or something. Hehe.

[sweetnsimple786]

Right, I can't find your actual unknowns for you. =)

But yeah, you can use matrices [Cramer's Rule] w/ a calculator program, but an easier way might be solving one equation for one unknown and then solving another equation for the same unknown and then equating those two expressions. That is...

3x + 2y + z = 4

x + y + z =2

2x - y + 3z =1

So I can take the first two equations and solve for z.

z=4-3x-2y

z=2-x-y

Now I set z=z and 4-3x-2y=2-x-y

So I just eliminated z from the mix. I can simplify that equation and have just x and y and use the third equation that I haven't touched yet to get another equation for x and y. Then I have two equations with just x and y in them. I can solve these equations by substituting or another method used for solving a system of equations. If you don't know what I'm talking about, you can google/wikipedia 'solving a system of equations'

[Bee.talbot]

Oh, of course!

So in this case, I would do

A + B + 2C = 16.4, etc. and then do all that magical algebra until I've found A, B, and C.

Then I can use the values for my model. Ah, that certainly demystifies the Logistic. Thank you!

[sweetnsimple786]

Erm well...

made up point: (1, 2)

2=A/1+Be^(1C)

2+2Be^C=A

This is why you don't want to solve for C first... it's just more complicated because you're going do have to add natural logs into this.

So yeah, do the magical algebra. =) & no problem