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Maths Portfolio - SL TYPE II BMI

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Introduction

Body Mass Index Body mass index is a measure of one's body fat. It is calculated by taking one's weight(kg) and dividing by the square of one's height(m). The table(Figure 1.0) below gives the median BMI for females from the range of 2 years old to 20 years old in the US, in the year 2000. Age (years) BMI 2 16.40 3 15.70 4 15.30 5 15.20 6 15.21 7 15.40 8 15.80 9 16.30 10 16.80 11 17.50 12 18.18 13 18.70 14 19.36 15 19.88 16 20.40 17 20.85 18 21.22 19 21.60 20 21.65 Figure 1.0 In this investigation I will examine a variety of functions to mathematically predict the fluctuations for the 'average' American female's body mass index. The parameters that are used in this graph are the Age which is represented in years and will be the X-Axis on the graph, and the BMI(Body Mass Index) which is given to 4 significant figures and will be placed on the Y-Axis. ...read more.

Middle

However I am positive that if more data concerning the BMI of American women were given, they would not match the Quintic model I have derived. From the suitable functions listed previously for this type of data (Quartic, Quintic, Cubic, sine and Gaussian), I decided to model the Gaussian since it fits with the original data very accurately as well as the Quintic modeled data, thus making it an appropriate choice. The equation for the Gaussian function is: By using the curve fit function on Logger Pro for the Gaussian equation I was able to determine the values of Figure 1.5 Values for the Gaussian Equation as produced by Logger Pro. Figure 1.6 Gaussian Function produced on Autograph, with Quintic Function and Original graph. The green curve represents the Gaussian function while, the blue curve remains the Quintic function; with the purple line representing the original graph. There are hardly any differences for this current range of data between the Quintic and the Gaussian function, however I predict that as the age increases the differences between the Quintic and Gaussian function will definitely increase greatly. ...read more.

Conclusion

I think my model fits this data reasonably well, although there are a few minor hiccups. After reviewing the data from women in the US and girls from China, it is safe to say that the quartic and Gaussian function are reliable enough to model their BMI from age 1 to 20. However anything after that is unsure of. There are a few reasons why the data from girls in China does not match those of the curves of the model such as the data being taken from the year 1995 In comparison to the year 2000 for the American women. The girls/women from China are also not divided into one group, however they are separated into two groups; urban girls and rural girls, thus making it slight inaccurate and difficult to compare. The variables of the girls are not known as well, which also make It hard to contrast. To make the model match the data of the girls from China, a simple shift down the Y-axis would have to be made, therefore connecting the girls from China data on to the quintic and Gaussian model. ?? ?? ?? ?? SL TYPE II BMI ...read more.

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