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

Math Portfolio - Type II

Extracts from this document...

Introduction

Introduction

In this Type II Math Portfolio, the task is to create model functions that fit a data set. This data set is the median Body Mass Index (BMI) of females aged 2-20 in the USA in the year 2000. It is then necessary to comment on the reasonableness and differences of these models and how they compare to the data set.

Using technology, plot the data points on a graph. Define all variables used and state any parameters clearly.

Logger Pro 3 (LP3) was used to plot and graph points.

image00.png

Figure 1

The variables and parameters used for the data points given are as follows:

x = the age of females in the U.S. in the year 2000

Where { x ∈  Ν⎮ 2  ≤  x ≤ 20 }

y = the BMI of females in the U.S. in the year 2000

Where { y Q ⎮ 15.20  ≤  y  21.65 }

Where Q = (a/b), a N, b N

For any curves of best fit being used:

x = the age of females in the U.S. in the year 2000

Where { x ∈  Ν}

y = the BMI of females in the U.S. in the year 2000

Where { y Q }

Where Q = (a/b), a N, b N

...read more.

Middle

15.40

15.44

-0.04

8

15.80

15.81

-0.01

9

16.30

16.30

0.00

10

16.80

16.86

-0.06

11

17.50

17.47

0.03

12

18.18

18.10

0.08

13

18.70

18.73

-0.03

14

19.36

19.35

0.01

15

19.88

19.92

-0.04

16

20.40

20.43

-0.03

17

20.85

20.88

-0.03

18

21.22

21.24

-0.02

19

21.60

21.52

0.08

20

21.65

21.70

-0.05

Use technology to find another function that models the data. On a new set of axes, draw your model function and the function you found using technology. Comment on any differences.

Using LP3, the Gaussian function was used to model the data.

image03.png

Gaussian function: y = -6.933e

As shown, there is very little error, as the RMSE value is close to zero. Therefore, the differences between the curve values and actual BMI values are very small.

Use your model to estimate the BMI of a 30-year-old woman in the U.S. Discuss the reasonableness of your answer.

The quintic model’s x-axis was change in LP3 to include the age of 30. The graph was then set to “interpolate” to generate an answer on the quintic function for x = 30.

image04.png

...read more.

Conclusion

When graphed against the Gaussian model:

image07.png

This model fits the data, although not as accurately as with the U.S. data, However, the Root Mean Squared values are both fairly close to zero (0.08161 and 0.2827). The same limitations apply to this data as the US data,

Conclusion

It was found that many model functions may fit a certain data set. However, when it comes to choosing the right function to represent it, one must explore the context in which the data set is given. Since the data set was the BMI vs Age, one needed to use reason in determining a suitable model function, and deduce any limitations. With such little data given, limitations can be found everywhere. If there were, for example, more ages and median BMIs, there would be a better fitting function available than the ones mentioned. It is important to note that through mathematical analysis and the use of reason the best answer can be reached.

Works Cited

James, W. Philip T. "Comparative quantification of health risks." 14 April 2003. World Health Organization. 16 December 2008 <http://www.who.int/publications/cra/chapters/volume1/0497-0596.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 ...

    function to the same domain and range as the domain and range on the scatterplot, the graph is as follows: The refined equation fits the data much more closely at the beginning, yet around the Age = 13 mark it starts to deviate again.

  2. Extended Essay- Math

    ��U�B�S��CUhg�`:.�K�aqfrt��� ���qß��y��f��M�ß\"� ��nqyo�a��m��Q9����� �Ê'D�DW��))T^8�Kq�W_��...Ѱ�ô3ea�"�<��Y�" �' ��T8��"��Y��5lo�_�<���;���"D?|F���.a��jZ�L�...4״����>��,�'�(r)>� ��� I��0R�4-�2P\1/2 Z5A_'�-�3/4|4�a3�'���4� �; �-(c)�%@�a���)'H&-�Y4l5��h{È°g/�7��%W�O��j]X� �D� ���T�3/4�n$8)>g-ÊO�1/4"5yD�5G=(c)����"w<(r)�6���� p�O-�R���oi^���)1v>��'L�������-"(tm)����|YS+FR�S�JT$�0�ec[iv�z1/4�w ar��2���...�-��Q ��H'��Â��Y:V �d(r)(r)cK����'�"ÛT�[wIov3w1/4m���=�}�l�F1/20�L(r) ��th��B+����� M_á±ï¿½N�;F[�(���N�o �-�1/2>���-����} �r�V��v8������' "Wo{>�z!r �%VyG0J�Y2��v �q@�W���b'tR(tm) @1� V!��<��q�71/4���sq{��~�χ�ݺ��H[?�S �z�"���{�7{�K{�BQ�.P��"W��o�13Z�QX�o��"w�=J�-ع��3/4�@?�4�Q��a���o_��p��%�K�+�...4�u��C�+6�...���Þv��{�xØ ï¿½t�*[�ÐZ��[gP���9��ӭ9FÊ�~�(�_La�e� �w ��yIf2�Â��(tm)cFpb�� �#s� �Z��� �j��^2I�y�x)U"|�5 ��g^Y{�vC"�sæ�e�\-5�$]��æG21/2k���t�I��`�zpv�~oQtϨ+ jLQY�2-�\��y|�+�Z"IS"Me���!C�`��"��J�� _&�AH��+�h�6Pk'��"ud...>-"ᵱ߸�� �h�F��o*'��Z)���G���"x|��wBOq�u�-ÔÑs~ì±E...�*�#(c)�"È�3/4(c)(tm)��?O` �b]c@t,��=Q3�d��{�{���~$�"-~���:����K%��_�v��H ��m ���R�mX�>� �\������?/-_'���k�GÄb#��Ý�QzU3�BRá£W (tm)��Q��7�bn"x�ܨ�?=�f5������M�������(r)�r _-�P uh� ��{u'@?��"G,� 3��qh��;�|�2�,���(wz�Z+7�r���j}�Mk{rWR��I ��ju���3=�Sh��A�s�\�ti�p��>.�6����`��:`��/H��X�y?D��8ѱ�w��xC� <B$-j ��z�6�Qs�v�����@�1/4i?x3/4]��yX�s�O�3/4� l�v1/2I���F�f�X?��>�(tm)tu�e�x-(c)�

  1. Math Portfolio Type II Gold Medal heights

    (Add other things) A sinus function might seem a reasonable solution as one can see fluctuations that produce an wave like form, however the general trend towards a greater height would not be depicted when using a sine function and the annomalties do not reoccur regularly.

  2. A logistic model

    65000 60000 55000 50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Year Figure 4.2. Growth factor r=2.3.

  1. Math Portfolio: trigonometry investigation (circle trig)

    0.883022 1 -140 0.413175911 0.586824 1 -120 0.75 0.25 1 -100 0.96984631 0.030154 1 -90 1 3.75E-33 1 -80 0.96984631 0.030154 1 -60 0.75 0.25 1 -40 0.413175911 0.586824 1 -20 0.116977778 0.883022 1 0 0 1 1 20 0.116977778 0.883022 1 40 0.413175911 0.586824 1 60 0.75 0.25 1

  2. Artificial Intelligence &amp;amp; Math

    This could be achieved with a security feature embedded in the computer's operating system. This security feature would be hardwired and protected from being tampered with by users. It would notify the ISP, through the Internet, if security flags were raised and, in turn, police would be notified. Solution outlined.

  1. Stellar Numbers math portfolio

    In this case, g=2, and s=12. Now, by substituting in 2 ordered pairs in the equation, two equations are created with only b and c as the unsolved variables in each. From here there is a system of equations that must be solved, and then the values of b and c are found.

  2. IB Math SL Type II Portfolio - BMI Index

    This gives me 0.21 for the period. Then to find the vertical shift I will simply add the amplitude to the y-minimum: 3.22 + 15.20 = 18.42. Finally, to find the horizontal shift (c) I must see how much I need to shift the graph so that it is aligned with the model function.

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