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# Math Portfolio - Type II

Extracts from this document...

Introduction

Introduction

In this Type II Math Portfolio, the task is to create model functions that fit a data set. This data set is the median Body Mass Index (BMI) of females aged 2-20 in the USA in the year 2000. It is then necessary to comment on the reasonableness and differences of these models and how they compare to the data set.

Using technology, plot the data points on a graph. Define all variables used and state any parameters clearly.

Logger Pro 3 (LP3) was used to plot and graph points.

Figure 1

The variables and parameters used for the data points given are as follows:

x = the age of females in the U.S. in the year 2000

Where { x ∈  Ν⎮ 2  ≤  x ≤ 20 }

y = the BMI of females in the U.S. in the year 2000

Where { y Q ⎮ 15.20  ≤  y  21.65 }

Where Q = (a/b), a N, b N

For any curves of best fit being used:

x = the age of females in the U.S. in the year 2000

Where { x ∈  Ν}

y = the BMI of females in the U.S. in the year 2000

Where { y Q }

Where Q = (a/b), a N, b N

Middle

15.40

15.44

-0.04

8

15.80

15.81

-0.01

9

16.30

16.30

0.00

10

16.80

16.86

-0.06

11

17.50

17.47

0.03

12

18.18

18.10

0.08

13

18.70

18.73

-0.03

14

19.36

19.35

0.01

15

19.88

19.92

-0.04

16

20.40

20.43

-0.03

17

20.85

20.88

-0.03

18

21.22

21.24

-0.02

19

21.60

21.52

0.08

20

21.65

21.70

-0.05

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.

Using LP3, the Gaussian function was used to model the data.

Gaussian function: y = -6.933e

As shown, there is very little error, as the RMSE value is close to zero. Therefore, the differences between the curve values and actual BMI values are very small.

Use your model to estimate the BMI of a 30-year-old woman in the U.S. Discuss the reasonableness of your answer.

The quintic model’s x-axis was change in LP3 to include the age of 30. The graph was then set to “interpolate” to generate an answer on the quintic function for x = 30.

Conclusion

When graphed against the Gaussian model:

This model fits the data, although not as accurately as with the U.S. data, However, the Root Mean Squared values are both fairly close to zero (0.08161 and 0.2827). The same limitations apply to this data as the US data,

Conclusion

It was found that many model functions may fit a certain data set. However, when it comes to choosing the right function to represent it, one must explore the context in which the data set is given. Since the data set was the BMI vs Age, one needed to use reason in determining a suitable model function, and deduce any limitations. With such little data given, limitations can be found everywhere. If there were, for example, more ages and median BMIs, there would be a better fitting function available than the ones mentioned. It is important to note that through mathematical analysis and the use of reason the best answer can be reached.

Works Cited

James, W. Philip T. "Comparative quantification of health risks." 14 April 2003. World Health Organization. 16 December 2008 <http://www.who.int/publications/cra/chapters/volume1/0497-0596.pdf>.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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