• 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...

Introduction

Math portfolio SL type 2

Shiba Younus

IB 2

Katedralskolan

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)

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

image00.png

Using graphmatica the data points were plotted on a graph:

image01.png

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.

Middle

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

image02.png

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.

Conclusion

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

image07.png

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. IB SL Math Portfolio- Body Mass Index

    Age (yrs) BMI 2 16.0 16.0 16.0 15.6 15.3 15.3 3 16.0 16.0 16.0 15.6 15.3 15.3 4 16.0 16.0 16.0 15.6 15.3 15.3 5 15.6 16.0 16.0 15.6 15.3 15.3 6 15.3 16.0 16.0 15.6 15.3 15.3 7 15.3 16.0 16.0 15.6 15.3 15.3 8 - 16.0 15.6 15.3

  1. A logistic model

    , (6 ? 104 , 1) 2,9 2,8 2,7 2,6 2,5 2,4 2,3 2,2 2,1 2 1,9 1,8 1,7 1,6 1,5 1,4 1,3 1,2 1,1 1 Plot of population U n versus the growth factor r Trend line y = -4E-05x + 3,28 0 10000 20000 30000 40000 50000 60000 70000 Fish population Un Figure 5.1.

  2. Body Mass Index

    old woman in the US using our model her BMI would be 18.64 kg/m2. In order to get this number we substitute the x in the function with 30 (the age of the woman) as follows: This result would not be reasonable or very convincing for many BMI researches.

  1. Maths BMI

    19.23 16 20.00 17 20.85 18 21.77 19 22.76 20 23.83 3. On a new set of axis, draw your model function and the original graph. Comment on any differences. Refine your model if necessary. From the equation y= 0.368x2 - 0.368x + 16.47, I put all the points in

  2. Math Portfolio Type II Gold Medal heights

    The Rage however stays . So now in order to find a suitable logarithmic function with the format of to fit the data from Table 1.1 the system of equation is used. Only the parameters of b and k were used, since they give one enough room to model a

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