• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

IB SL Math Portfolio- Body Mass Index

Extracts from this document...


“Body Mass Index”

BODY MASS INDEX                                

Throughout this portfolio, various functions will be evaluated, applying the given data.
A model function will be determined and extrapolated as it relates to the following real-world example:

Body mass index (BMI) is a measure of one’s body fat. It is calculated by taking one’s weight (kg) and dividing it by the square of one’s height (m).

The table below provides the median BMI for females of varying ages in the US in the year 2000.

Age (yrs)








































(Source: http://www.cdc.gov)

When graphed:


(The independent variable being the age of the women studied <x>, and the dependent being the BMI of these women <y>. Both values must always be greater than zero. )

This graph’s behavior is most nearly modeled by the cosine function,image01.pngimage01.png, because it is undulating and periodic: it repeats a pattern as it rises and falls. However, due to the limitations presented by the nature of the given information itself, only the portion of the

...read more.


through trial-and-error, and decided that the function
f(x) =3cos(.2x-4)+18most closely modeled the data, though certain values did not perfectly correlate. Below is a graph showing both the given BMI data and this model cosine function, for comparative purposes. It can be seen that the actual raw data very nearly coincides with the model: they curve in a relatively similar fashion, for example. The graphs are not, however, identical. Certain points do not exactly line up with this model. The first few, for instance, before age five, have slightly higher x-values than the cosine model, as do the last few, after age sixteen. Other values also do not correlate perfectly. Nonetheless, the model illustrates the provided BMI statistics with relative accuracy.


In order to discover a different function that models the given information, I used technology.  I downloaded Graph 4.3, and saved the given data, the cosine function, and the model function into the program. When I compared the graph of the BMI statistics with my own model, I noticed that they did not look as

...read more.


 to be a bit of a closer match. Below is the data graphed with this new model function, for comparative purposes.


It can be observed that this model does not perfectly correlate with the data, but does reflect its trends with relative accuracy.  Because the data for Guatemalan women was more sporadic than the data for American women, it was much more difficult to discover a model that fit. In other words, the data did not always follow a consistent undulating pattern, while the first set did, making it harder for a function to correspond. There was also less data present, as there is a gap between ages seven and eleven and it stops at age eighteen, which also made it difficult to view any trends. The data often shows slightly higher x-values than the model, and at some points, they are lower.  Because I used a trial-and-error method (on both a GDC and the program Graph 4.3) to discover it, the model function I found may have somewhat limited accuracy, though it does illustrate the trends this data presents pretty closely. The function, while not a perfect match, is appropriate considering the limitations presented by the data itself.



...read more.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. This portfolio is an investigation into how the median Body Mass Index of a ...

    Using those values, the range of a curve fitted to this data should be: {} Judging from the distribution of data, the pattern created looks very much like that of a sinusoidal function. Based on this assumption, Finding the values of a, b, c and d in the function should result in a graph that fits the data points.

  2. Extended Essay- Math

    9�-��"p�:���&y�{��(tm)�(���9�� d^��*"d...�...�#��"Z-�$�G1/4kBS��d��T�1/2�i�(tm)"���9��"�LÏ�78�s��`��q��K��'Jm�-V�W�(c)�?���`uwíºï¿½"Fj��-X.�1/2�Ü�3/4���Þ��4���,�_;�2�=�xt�)�(tm)��#"�^{L�Ng(�]� b_�_UK1/4�e߸W�V��T~nl�my����YV4(A� �AxHr�R j��_�9`C8>�������M�PC�u��]��E�`$1L�1-�5����8K�Q�^� p �44g�4�D�,��C'��:]1/2*}'�-��F}N /3e333׳�<g�gcfkc��9�8ݹ\7�c[�������<*�-�$B#�^�O�V<O"V�G�^�DF[VMNE^UAS�P�Fy�J"j(r)Z��#�--e�H����9�c�b&�"�ZU-��v6E��wm��:�;�rz�������*��1/4�1/4E|b)7|��u�{� T-�s�"��5'��1q�{^$�'���L�(tm)�(tm)��1�%��1/4ol�|n��/y���×��=�zl���$�t�\*��$3/4*����u5̵yu�� 1/4�×l��['.��3/4��z�ݧc��� î­*\{�3/4�~��"�2(}(r)�=�8v�(c)�30Q�Bc��"o��1/4;�^kfa��1/4�Ç...����XÜ¿tyy��ܷ���"J?���l\��(c)3/4u�-�%�3� ��$�X?j�&`,� ���'��e"�������-@� ��cz�5&�K�:`˱�p2�4�#1/4(> �-`F�B#LSId%� e�� �'����n�[Ó¿A� z�&� y�(c)�Ùy(tm)���...���ˡ��"+�Û� ��M3/4�1H�,�)�F��i��b�â�(c)�k�O2rdyiKdE)w"|V�Ww�(��f���m�[7�3l4&�"�>3���cem=aK�����N�\ ���Wv_���V�Y���- h ' (r) m-��2��� ��&T'$�IMJæd2g���i��:�0�/:|����xeo�\ib�l...G�X��(c)og�jq� �}�wkh1/2���<Þ¢q���Õk����;;�"o߬1/4E�"��k��"g�'��<X}6�~����1�'�Æ��{(r)��p��+��o^1/2�y->=2#�!i��1/4��"O= [_��\t_r_����Mh���{�j���kY?�?Ϭ֣×on"o�m�m��|�%�E�j�Z�V�N�3/43/4c��@%Å�@��������� �<3/41/21/2^1/21/21/2Y��7�����+v���(tm)�Ét'���7���� ��s�c�b pHYs �� IDATx�]}pW�NH ...�"�$RHA�"v�MI�"8��dj;��PGj�(c)v�~e� Z&�h�Gu��?��N��Ȩ��L�h�"3�DFQi ���R$� �������~���8"���}��s��ps�g�VNLLT�H���t\A�M*x-'�@B ��8�]�0.<�PH�":�fF�".� �&:����... � �³ E�"N��hvaH�¸ï¿½lB ��8�]�0.<�PH�":�fF�".� �x�7Ö¬Y�?#�͢-�(r)

  1. Infinite Surds (IB Math SL portfolio)

    1+4k = m2 4k = m2 -1 Thus, k = > Test the validity of general statement using other values of k The general statement: k = Testing 1) If k = -5 -5 = -20 = m2-1 m2 = -19 So, there is no value of m.

  2. Math IB SL BMI Portfolio

    If a curve was fitted to this data, the domain should be: {}, those values being the lowest and highest ages given in the table of data. The lowest y-value on the scatter plot is the data point at 5 years (15.20 BMI); the highest y-value on the scatter plot is the data point at 20 years (21.65 BMI).

  1. Math Portfolio: trigonometry investigation (circle trig)

    The relationship between the uses of x is that to see the pattern repeating. The period in the graph is which approximately 6.28 when expressed to radian are. The frequency refers to how many cycles a graph have gone through.

  2. Shadow Functions Maths IB HL Portfolio

    C.1 Two Complex and Two Real Roots Let us start with the first case, by considering the function where . The function has two real roots and two complex roots . Its shadow function is sharing the same real roots but instead of two complex roots it has two more real roots .

  1. Gold Medal heights IB IA- score 15

    Lastly it hits a maximum point with slope zero and the curve goes down into a negative slope. This would best represent the curvature of the data collection because it follows the same pattern as the sine function. Upon observing the points (1932, 197), (1936, 236)

  2. Mathematic SL IA -Circles (scored 17 out of 20)

    diagram: Length of OP Length of r OP=?r First test 4 2 OP=2r Second test 3 4 OP=r Third test 5 7 OP=r Fourth test 1 3 OP=r According to the diagram shown, we can know that C1 and C2 don?t intersect at one point when OP=r.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work