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IB Math SL Type II Portfolio - BMI Index

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Introduction

IB Math SL Type II Portfolio

January 14, 2010

        In this portfolio, we will look at the median BMI indexes for females between the ages of two and twenty in the US in the year 2000; and from this data, a model function will be determined.  Body mass index (BMI) is a measure of a person’s body fat, and is calculated by this formula:

image00.png

        Looking at the data table we can see that there are two variables:  one being the age (in years), and the other being the BMI.  The independent variable is the age and the dependent variable is the BMI, since the BMI’s of the females depend on what age they are.  The parameters are the weight and height of the females, which both directly affect the BMI.  After using software to graph the data points, I believe the graph’s behavior is best modeled by the cosine function, since it has a wave-like shape and is periodic.  Next,

...read more.

Middle

image02.png

My model function is:

f(x) = 3.22*cos(0.21x – 9.95) + 18.42

As you can clearly see, the first model function fits the data almost perfectly, but it is very unrealistic for predicting BMI’s of women, as it just keeps rising and falling; so it is virtually useless for estimating the BMI of a 30-year-old woman in the US.  This is fairly obvious when looking at the cosine graph, as you can see that a 30-year-old woman has a lower BMI than a 20-year-old woman.  This is essentially impossible unless a woman became shorter and/or lost a lot of weight.  It would even be reasonable if a 30-year-old woman had the same BMI as when she was 20, but it is much more likely that she would have a image03.png

slightly increased BMI, at the least.  I believe

that a linear function will do a much more accurate job in predicting the BMI of women in the US, but only for several years

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Conclusion

/td>

16.2

5

16.0

6

15.9

7

16.1

8

16.5

9

17.1

10

17.4

11

18.2

12

19.2

13

20.1

14

21.0

15

21.3

16

21.8

17

21.9

18

22.2

19

22.7

20

22.7

(Source: http://www.archive.official-documents.co.uk/document/doh/survey97/hst3-4.htm)

This BMI data for females aged 2-20 in London fits my model to a certain extent, as it also follows the same trend.  However, you can see from the graph that the data points from London are just slightly higher.  To fix this, a simple change in amplitude and vertical shift would be sufficient.  Well, the biggest limitation on my model is that you can’t accurately predict the BMI for all ages of women in the US.     image04.png

...read more.

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