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

BMI; math portfolio type 2

Extracts from this document...


Math portfolio SL type 2

Shiba Younus

IB 2


Date: 08-06-09

Body Mass Index

The table below gives the median BMI for females of different ages in the US in the year 2000.

Age (yrs)









































Using graphmatica the data points were plotted on a graph:


The BMI data provided is confined to females between 2-20 years of age in the US. No data for ages below 2 years or above 20 years is available. The variables age and BMI, as appear above, are along the x and y axes respectively.

Since the graph appears to resemble the curve of a polynomial function (studied earlier in the course) and since these functions are easier to work with algebraically, I decided to work with

...read more.


15.70= a33 + b32 + c3 + d…………...1 (x = 3, y = 15.70)

15.30 = a43 + b42 + c4 +d……….2 (x = 4, y = 15.30)

20.40 = a163 + b162 + c16 +d…….3 (x = 16, y = 20.40)

20.85 = a173 + b172 + c17 +d……...4 (x = 17, y = 20.85)

The answer from polysimultaneous equation solver was:

a = -0.00439

b = 0.164

c = -1.38

d = 18.5

So the model function is: y = -0.00439x3 + 0.164x2 - 1.38x + 18.5


The model function fits the data points obediently.

Since the shape of the graph resembles the curve of a sine function too, therefore the sine regression function in the calculator was used to find another function that models the same data, and compared with the model function that was obtained algebraically: image03.png

Though the sine function shows a great deal of similarity in behaviour to the cubic function when it comes to fitting the data points, minor differences can be appreciated. There are noteworthy differences when it comes to y and x intersects of both functions. The y intersects for both functions differ by 0.

...read more.


2 + c(15) + d….4 (x = 15, y = 19.4)

The answer from polysimultaneous equation solver was:

a = -0.004, b = 0.15, c = -1.31, d = 17.9

The modified model function for this data is: y = -0.004x3 + 0.154x2 – 1.31x + 17.9


The modified model function now appears to fit the graph of the data well.

Limitations to the model function are:

  1. The model function is obtained from a specific combination of variables (x, y) since other combinations result in different behaviours of the model function.
  2. It is unique for the particular range of age provided in the data. This implies that the BMI for ages outside that range cannot be correctly estimated. As seen in case of the 30-year-old woman in the US (fig 1.4).
  3. It cannot be applicable to BMI data for females from another country. The model function needs to be modified to fit the data points. As seen in fig 2.2

References: 1.http://www.massgeneral.org/children/adolescenthealth/articles/aa_body_mass_index.aspx

2. http://www.ijbs.org/User/ContentfullText.aspx?volumeNo=1&StartPage=57&Type=pdf

...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 ...

    back down and back up for women ages 20 to 38 (the difference of 20 and 38 being 1/2 of the period). Because that data would be wrong based on the common knowledge of growth stopping after 20 years of age, one can conclude that a sinusoidal function will not match the data in the domain: {} .

  2. Extended Essay- Math

    B��IZ�--e8\����jr6;k�]�" '�� �4� 'qE��'o�7(tm)��bW���l�l���T-b0�b� �-"�XQJ�U�>Z�N�7�"0p�`�]߬7h�w�-T� +�''Fl.r8�^�[�RB��t0(tm)D-PsId��0����PK!x|(c)��word/footer2.xml�V]O�0}������iia)b... � U��7q�Ķ(r)Ý��]'m +L-hZ����s�-rq�\W�J��Z�$P��L�"&�-""sX�U�+�DL��'���/ ��,kL"�9������2mu�(c)(r)C��2a�! �4��� k1Ô"�dW���j�n��"��5-���g��P�7�Psg ô§¥9A��;���tk�G'=�*&KPl��W�}`"��-F���2�����"3/4A�s���ʵ�B��-�1/4��h��rKé¯_�mLt��O�!E��`�� �F2��(c)(r)�<��zi�?#z@E<D�� "1*L^7_��1/4tRcp�>3P� -�We�����S��-�������Q{"��F� N�]�4�E...�0��H2��d|d���b2�I2Nf��:��1/4�l�C+��-�� ��)=��{ӵ��r�o��4L"�$]�9�qܺ��UL���79�Z�_5���9-Ga���+�-��'� �Ö"(c)�a�W�,p;K...DQz�ָ�;d�B�N�9/��^t�CT�O��lN{NGx��*��0���qm0� �)�D�=E9xD�~�3kx��"�d:��1/2 ��L�wtX�"Å)(���h4:��> o Sz Z��tYw��� q�@��n��� ��; "�����f"�����@��gU%N�h��P��!�^�-NEۨ� ��/��o��PK!!Z�"! �word/theme/theme1.xml�YOoE�#�F{/�'M�:U�� �i��-�q1/4;�N3"��'� �G$$DA�Ä*�-�iEP�~���(r)w�q""4��;�{o�1/2?�g�\=J: BR�6��{�'4�MG��v�{i5@R�4Â��L� (r)n1/4��1/4(r)b'�(c)\�� V*[_X�! c�-�H �\$X��-D��"-,�j+ �i�R���[�! �k��F�1/4��1UR"L�j�Hl�_�9'm&�f��a�(c)1,1/4h5�,l\Y��Ssd+r]�-����(tm)S��nc��V(c)����u:�v�^�3��(c)�����]�� ���9""][(r)5\|E�Ò�k�Vky-��*5 ��1�_��461/4Y�� 3/4��l�W1/4Y�� 3/4{ym��� (f4ÝA�v"��2�l� _�j-�OQ� ev�)�<U�r-����@V4Ej''!

  1. Math IB SL BMI Portfolio

    value. Knowing that a sine function begins by curving up from the line of symmetry, the horizontal phase shift (c) value can be approximated by looking at what the x value is where the y value is � 18.425 and the graph is curving up.

  2. Math Portfolio Type II Gold Medal heights

    Though there is a general trend that suggest the height will continue to grow one also has to take into account that human bodies can only sustain so much strain. Considering that the strain increases with the height achieving a greater height will become harder and harder and at some point, a maximum height should be reached.

  1. Derivative of Sine Functions

    �repeat its values every 2,(so the function is periodic with a period of 2) �the maximum is 1 the minimum is -1 �the mean value of the function is zero �the amplitude of the function is 1 According to the characteristics the form of function for the gradient is similar

  2. Math Portfolio: trigonometry investigation (circle trig)

    0.8090=0.8090 When 77 is to represent the value of x and 13 is to represent the value of y in the conjecture sinx=cosy, sin(77) would equal to sin(13). Again this should add up to 90 degrees. sinx=cosy sin(77)=cos(13) sin ?=cos(90- ?)

  1. A logistic model

    Growth factor r=2.3 The population of fish in a lake over a time range of 20 years estimated using the logistic function model {7}. The interval of calculation is 1 year. Year Population Year Population 1 1.0?104 11 6.00?104 2 2.3?104 12 6.00?104 3 4.51?104 13 6.00?104 4 6.26?104 14

  2. Math IB HL math portfolio type I - polynomials

    a-bi is called the conjugate of a+bi, where a and b are real numbers and i = (?-1). Let a+bi denote a-bi. In other words, a+bi = a-bi. Prove that:_______ _____ _____ (1) (a + bi) + (c + di) = a + bi + c + di (2)

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