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

Math IB SL BMI Portfolio

Extracts from this document...


This portfolio is an investigation into how the median Body Mass Index of a girl will change as she ages. Body Mass Index (BMI) is a comparison between a person’s height (in meters) and weight (in kilograms) in order to determine whether one is overweight or underweight based on their height. The goal of this portfolio is to prove of disprove how BMI as a function of Age (years) for girls living in the USA in 2000 can be modeled using one or more mathematical equations. This data can be used for parents wanting to predict the change in BMI for their daughters or to compare their daughter’s BMI with the median BMI in the USA.

The equation used to measure BMI is:


The chart below shows the median BMI for girls of different ages in the United States in the year 2000:

Age (years)

Median BMI







































The values “height (m)” and “weight (kg)” can be discarded when trying to analyze this data because it is not consistent that a girl will have a fixed weight to height or vice versa when they are a certain age. For example, the median BMI for a 10 year old girl is 16.80. With only the data provided, one cannot isolate either the height variable or the weight variable using the formula for calculating BMI.

Using the computer program TI InterActive!™  to graph a scatterplot using the data, the resultant graph is as follows:


...read more.



b =image29.png

Using the approximated a, b, c and d values, the resultant equation is:


Using TI InterActive!™  to graph that function, the resultant graph is as follows:


Overlaid with the original data, and restricting the graph of the function to the same domain and range as the domain and range on the scatterplot, the graph of both the data and the function together is as follows:


Comparing the two graphs, one can see that where BMI = 18.4 in the function is around 0.400 years off from the corresponding point on the scatterplot where BMI = 18.4. 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 {image07.png} and {image08.png}. A slight stretch about the y axis would fit the curve closer to the data points in those areas, therefore the b value should be changed from π/15 to π/14. The number π/14 was chosen because reducing the denominator’s value by 1 will increase the b value by a slight amount, and an increased b value will shorten period and compress the graph about the y axis, resulting in the values within domain image09.png to be closer to that of the data points.

Making these changes, the revised formula for the sinusoidal function is as follows:


Using TI InterActive!™  

...read more.



"Body mass index." Wikipedia, the free encyclopedia. 16 Mar. 2009. 16 Mar. 2009 <http://en.wikipedia.org/wiki/Body_mass_index>.

"Logistic regression." Wikipedia, the free encyclopedia. 16 Mar. 2009. 16 Mar. 2009 <http://en.wikipedia.org/wiki/Logistic_regression>.

Mueller, William. "Logistic Functions." Exploring Precalculus. 16 Mar. 2009 <http://www.wmueller.com/precalculus/families/1_80.html>.

Shang, Lei, Yong-yong Xu, Xun Jiang, and Ru-lan Hou. "Body Mass Index Reference Curves for Children Aged 0-18  Years in Shaanxi, China." Department of Health Statistics 1.1 (2005). 12 Mar. 2009 <http://www.ijbs.org/User/ContentFullText.aspx?VolumeNO=1&StartPage=57&Type=pdf>.

"Sigmoid function." Wikipedia, the free encyclopedia. 16 Mar. 2009. 16 Mar. 2009 <http://en.wikipedia.org/wiki/Sigmoid_curve>.

Appleby, A., Letal, R., & Ranieri, G. (2007). Pure Math 30 Workbook. Calgary: Absolute Value Publications

Technology Used:

TI InterActive!™  Free Trial by Texas Instruments

TI 84-Plus Silver Edition Graphing Calculator

Microsoft Office Excel 2003

Microsoft Office Word 2003


Graph of Sinusoidal function in Blue followed by Logistic Regression function in Red, with the extraneous values removed.


...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 ...

    minimum, one can find the period of the function knowing that the difference between the x value at y max and the x value at y min is 1/2 of a period. The period of the function is therefore 30.

  2. Extended Essay- Math

    h�|�-���-��"��("1/4R�1/4��'�'s�L��l�����?Q���1���5ݦ�9AS6<�0;%4���&��0�ÛW~� Ô��3/4�Â#k-rbv�(tm)�ÚNC�1/2�p|�}�XE""C���Ç�� 74��׶ 7 nR����"��}"yO�� �m�Ni4�"�S@zY#"j�z��~��J��d���Yu�ha Ê'�� ��1/2�CBi�"z�>n�Ҹh�G�H��>Y(tm)]����PK!3"M�-� word/footer1.xml�U�n�@}����=xI�'ULD'E�"Ԥ��k{�E� ���,�&)I�Cy��x��93���"����'�NH�GI$tj2(c)�"�~���I�<��� �G(r)&_�\�,�a�v��iBJ�-�c--Bq�S2�L�{(c)Q��s(tm)��6���O�wL*��T7\��#;8e�CS<m��)ÇK�a22Vh�P�"��#�yiÏ��^.d%���Q �J�4�(c):�T...��JU�3�~�*(c)k.m}�drkҥ�o�� *$l�+����hX����O�/�ֶ?8�×ç¦ï¿½ï¿½ï¿½ï¿½m��-�1/2Q�� RUS�0P�1��O��H��8C�u�-���"?V��$�O�g ����TY�9�{��a...%p3:�-�-��I "��V�H��3/4���BFX�(L$(tm)�b�>2Ë�g N����`�b���V��/��J�)����V�|Y��7�`:���l�$��6��TW1/4J��/���M \�9�"8�9�h�:t��4� �`([�"ì³ï¿½ï¿½ï¿½,p;K�DQz�6��dhR�"�s^���Z4�cT1/4�jwÞ� '( �nJ �zw���X�...Qbȱ=EyxB�a�3gy��"�d2������9~&�;:6�S�d1/4-��`p1"(tm)N���m��ΰ ������� �"�XK�b��F ��z� ��PK!�D����word/footnotes.xml�XMn�6��-�Jd)���{ �'M� ��E�%#S1I��5��ܡ��Yz"9IiI�e'U&:�&��P�{��/s��C��'�r6p|�sa1�S�8�̦�g R�9�8#gM"�v��w�E�p(r)�D!��TX�x�Z���QqJr�Ü�'+�h7�y�' �I��r�9�|�&$��R p"� +�-�v�rW�O<�"c�j��� �&\�X+-����-� ��=ͨ^>�_�Y ��dai�qm�9�p�g�f���� ��Q��{�-�92��2'L[xI2�(tm)J(c)x��K�i�I���-"���W����c� �}��{� �1�ʳ & -¨)�ZxÄ�1���"�B�|�-Q�I...�|IB]J3/4�U�3/4L�{_�2���1/43/4M�m�Գ�Õ" � < ��K|�"`(tm)�t�[� �^ x"��k.X��s�Û���1/4"���nt:��&� V5� �jP~(tm)�P+���.<����Kc'�e���Ü%(w~wlJ�F��w@����*� ��9�"-m��5-� 1/4�F1/2�1/2�A ��6��

  1. Ib math HL portfolio parabola investigation

    Now for a cubic equation, we have 6 roots when it intersects with two straight lines. These six roots are X1, X2, X3, X4, X5, and X6. We can express any cubic equation in its factored form as: = a(x r1)

  2. Derivative of Sine Functions

    0.191 0.354 0.462 0.5 The scatter plots of values in the table are sketched below: (joined by a smooth curve): gradient of f(x) =sin-0.5x at every /4 unit b) Make a conjecture of g�(x) g�(x)=bcosbx c) Test the conjecture with further examples.

  1. Salida del sol en NY

    Algo interesante es lo que sucede cuando se traslada uno ya sea al oeste o al este, ya que en este caso la variaci�n en la salida del sol es poco cambiante solo se ve afectada por la inclinaci�n terrestre si careciera de esta, no importar�a si te trasladas oeste

  2. Using regression analysis to solve a real time problem

    The age of the drivers is observed to be negatively related to the number of times they had accidents and the Pearson Correlation Coefficient of 0.513 in absolute value shows that this relationship is a good one. Nevertheless, the correlation between each variable and itself is a perfect one with a Correlation Coefficient of 1.

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

    Volume of wasted space (m3) Max volume of cuboid (m3) Ratio Volume wasted : Volume cube 75 228230.855 311769.145 0.732 : 1 85 258659.557 353340.443 0.732 : 1 95 28909.494 394905.506 0.732 : 1 110 334740.665 457259.335 0.732 : 1 111 337781.665 461418.335 0.732 : 1 112.5 342346.282 467653.718 0.732

  2. Maths Portfolio - Population trends in China

    If we see at the beginning of the 1st picture of the linear function above, we can notice that the line is decreasing and eventually going towards the negative set of numbers. We know that this is not possible when it comes to the count and growth of population, so

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