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

Mathematics SL Portfolio part I

Extracts from this document...


Mathematics SL Portfolio part I

An investigation into the median BMI for females of ages 2-20 in the US in the year 2000.

Mathematical Modelling

Your body mass index, BMI, is an effective and easily manageable indicator of body fat. Today, such statistical guides are vital guidelines for a country’s populace and health system due to the ever-increasing rates of obesity in the more economically developed countries. Here, highly caloric food is not only abundant and overly accessible, but also inexpensive and, time-wise, favourably convenient. Nonetheless, overly large intake of such food, combined with the averagely low physical activity of our time, is often accompanied by various health risks. As the indicated amount of excess body fat increases, so does the possibility of various diseases and conditions, including type 2 diabetes (and all its sub-problems), high blood pressure, cardiovascular disease, respiration difficulties, osteoarthritis, strokes, some cancers and premature death.[1]These being far from trivial, a healthy BMI is generally a vital asset[2].

The following is a table that portrays the median BMI of US females between the ages of two and twenty years in the year 2000:


In this investigation, I aim to examine how models may be fitted to the data given and hence used to depict and predict fluctuations and changes in the BMI of females in the US.

I shall use a TI-84 Plus GDC and the electronic mathematical programme: GRAPH, created by Ivan Johansen and available at:http://www.padowan.dk/graph/ .

...read more.


Yet this process, despite being simple, is one prone to many careless mistakes due to its length. As exact values are key in this highly specific model, it is far more advisable to solve the system using a neater, shorter method:

When having two or more equations, we may solve them through the use of matrices. The availability of a GDC simplifies the process even further;

With the four equations in four unknowns, we enter them in a 4 x 5 matrix (in our case: [D]), placing the constant in the far-right column:image02.jpg

We then »quit« this area of the GDC, return to MATRIX, move over to the MATH menu and take choice B: rrf( , press enter, then insert the matrix name ([D]) . Upon pressing ENTER, the whole system will have been solved for you.

Yet the most appropriate way would probably be the GDC’s cubic regression option which calculates the best fitting function using the given points: from having entered those points into the STAT option under L1 and L2;image03.jpg

  We return to the  statistics menu (under STAT), go to the CALC submenu, then select CubicReg. We then enter the commands; L1, L2,Y1 and, upon pressing ENTER, attain the image below:

From the general equation of a cubic functionimage05.png, we have now derived that: image04.png

a=-0.0040727906,  b=0.1535049941,  c=-1.275202327 and that  d=18.27170795, giving us the function:




...read more.


The data for females in 1995 was as follows[3]:

Age (years)

Median BMI(kg/m2)


































In Due to the previously mentioned lifestyle and physical factors, we may observe that the median curve for Guatemala indicates, when compared with the US median, a lower BMI at the younger ages, then a steeper rise in body fat leading to a median of higher BMI in the later stages of the female development. Due to this specificity of backgrounds, the model of the polynomial to the third degree for the USA is not applicable in this case, however, as we are indeed all of the same species with generally very similar characteristics and not overly large amounts of variation, such a cubic function is still applicable, it need only be adapted to the data for Guatemala to attain the appropriate curve.

Bibliography: http://www.unu.edu/unupress/food2/uid02e/uid02e00.htm#Contents



[1]  Obesity and Overweight. World Health Organization: 2009. Available at: http://www.who.int/dietphysicalactivity/publications/facts/obesity/en/ Cited: 07.11.2009

[2] Exceptions where BMI may be unrelated to the probability of the said conditions due to physical deformations have been known to exist.

[3](the data missing is not of vital importance to the situation)Data attained from:  http://www.unu.edu/unupress/food2/uid02e/uid02e00.htm#Contents

...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 ...

    That can be fixed by adjusting the horizontal phase shift value of c to 12.4 to compensate. There is also a noticeable discrepancy between the function graph and the scatter plot in the domain {} and {}. A slight stretch about the y axis would fit the curve closer to

  2. Extended Essay- Math

    ���L��(tm)����ֲٲ�_�"�<��Ý�'W'"���T +X*d+t),+J*�)V*>Q")(tm)*e(u(-)K) (�R�PaR�Q9 ҧ�(c)���zQu^MX�G��3ufu;��� C� �k���q�W4��'� �jÔ�� �(r)Õ�ԡ��(tm)����=�;�' G�"�{�/��_�?k ab�d��P�0ư�p�H�(ͨ�elf|�x�"l�lRa��T�4���(tm)�Y�Y�9�����3 - ?��EK5�4�~+Z+G" "w�'�1�]6���M'�K[��]`-�(r)�]�����(r)�c���+�?8(8�u������������Ӥ��s1/4s� 1/2��K�˪"�k��"��[��wNw�{� ��ţ�ce���"g<U<s=�1/2�1/4'1/4������71/27����է�g���RMY��=�"�g�W��_߿�>@' 0`6P'�0p.H'�(h>X/�$x�jD� ....��� Y �z>t;�5�%��A����L�|%�5�}"z1�*�.����cF'áx��ot*~$�$^MbL�HJ-L�K�M1M9-�N�K��+�7k��4����P�oz_�PFN�L�Yf}MVh��l����o�\�u���d�L�7�!-.7&�����R �)��m�?t?_>�$���G�"�.,>�z��1ì±c����2�N���*�v��1/2�'Ó¥4��Se�e�����7*�+�VV���>(tm)wr�ʿj�"�(c)��yN�y�zf��ٶj��'lMBÍZ-�"���5�q���m��8?U�P�� �����x�|!��|"g�H�qs�E(tm)�g[X[�/�K�->^��<~��J�U�"��\;���z� jKn[ln��p�x�i��ץ��z]���7*o��<�MÓ�1/2}+��JOT�BoP�t�w��m��O�� ��޹}���A���4�u�W��@�AÛ�P�C���ê�m��-u�h�t=�~�=�7�;f<v��" Om�>-w-�x�lj�b�y�� /�'3_b^-z���5���7oZ�T�n3/45~;��������7fr>�>"���6�)�Ý7�����̧�O� ��?��"���_� -�-�,�,m/���7�o}+v+���__=��G����Ý(r)?g�7pe��][V[/�÷��(1"_� i�@-�#5";R;�@C�"��Å"+Â` !�-6'��a� �A�0 ��Ө�2:#�(tm)�V�B��Q:"L�"1�I�[0�0�%�b�e�e1/2Â���������]�x �)|N"Y,S|V�V�E�N�O���-R��i�~Õ·jk���Z'��:ƺ�z-�� ��F%�&]���^��Y�Z��l�m�v)�i�:X8�:98;"�����"{xx�����������@��5��W � � b ��S�"1/4 }vY�""��D'�Pb �8�3/4�&"&F&Y& %o�<Km�{0�']-� Y[׳ �����0�����-:|P;�5o3}X�H�Q�cW�o�K��-'/U(S*W(r)P(c)T9(c)Z�y��t�(tm)��5,��1/4�"Χ��6o�1/4p(r)(c)�����-�K��\��6�&�-�Q����ì­n�[ =.1/2...}s���w-�};�x�@d��p죰��j�1/4c4ckO��>���k���[/z'"_�1/4:�:������'w���+g�}�?�<>����"�y���;_j��] Y�]V�*�Mb��{����o686ݶj��w�'%:��>@bP$�s���2* �}#����dq_�}"*�4�?��'Î�-!�1�\�4��U�Í1/2���Û�0�0?I�^�ÐQ�D,A1/4N��7iqYe9 y %E %^eH�� �[ jtj6hUh�����ַ504T3'56�4e0Ú��/Z�XNX Yw�\���Ud-c�@q�s�u-rawŸ.�1/2t��g�W�-/oi ��+�^�Ú���A6�rTF�×��mae��n'�Q��[1E��q*��"s��I&����)WR3�ڦq�}L��8''�m�x��~�\�R

  1. Math IB SL BMI Portfolio

    The period of the function is therefore 30. One can find the value for b using the formula: b = Using the approximated a, b, c and d values, the resultant equation is: Using TI InterActive!(tm) to graph that function, the resultant graph is as follows: Overlaid with the original data, and restricting the graph of the function

  2. Modelling Probabilities in Tennis. In this investigation I shall examine the possibilities for ...

    shown graphically: This shows that when the point probabilities are close to each other (i.e. near 0.5) a small change can make a large difference in the overall game probabilities, whereas if the point probabilities are far apart a change will not make much difference.

  1. Maths IA Type 2 Modelling a Functional Building. The independent variable in ...

    143.178 72 2.5 25772.078 10308.83117 5 12.5 141.421 72 2.5 25455.844 10182.33765 6 15 139.642 72 2.5 25135.632 10054.25283 7 17.5 137.841 72 2.5 24811.288 9924.515102 8 20 136.015 72 2.5 24482.647 9793.058766 9 22.5 134.164 72 2.5 24149.534 9659.813663 10 25 132.288 72 2.5 23811.762 9524.70472 11 27.5 130.384

  2. A logistic model

    as the rates are first very high, but are then very low in the next year. This means that in year 11 the rate of deaths is very high (or that of birth very low, or possibly both) and hence the population in year 12 is significantly lower.

  1. While the general population may be 15% left handed, MENSA membership is populated to ...

    However, in the chi-squared calculations done by hand () in Table G, the values were used to three significant figures (see Calculation of Expected Values, page 11) for more accurate data. Degrees of Freedom The degree of freedom dictates the acceptable amount of variance in the final statistical calculation.

  2. IB Mathematics Portfolio - Modeling the amount of a drug in the bloodstream

    Also, in the data given there is a little minor mistake. Between the 7.5th hr to the 8th hour after the initial dose of drug, the amount in the blood stream remains the same. I thought it might be a human error because I didn't think the amount of drug would stay the same for that specific hour.

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