• 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. A logistic model

    The steepness of the initial growth is largest for figure 4.3, and so is the deviation from the long- term sustainability limit of 6x104 fish. 10 IB Mathematics HL Type II Portfolio: Creating a logistic model International School of Helsingborg - Christian Jorgensen 5.

  2. Maths BMI

    + 18.81 with an RMSE of 0.04725, which is also more accurate than the cubic function, but not as accurate as the quartic function. The quartic function is the most accurate so I will use this graph for the following question.

  1. Math Portfolio Type II Gold Medal heights

    Therefore a Domain can be stated as with the restriction that and . Also as previously mentioned the Rage must be limited to since a jump cannot reach its maximum height at a point lower than the starting point. A linear Graph will not be suitable as one as well

  2. Math Portfolio: trigonometry investigation (circle trig)

    is negative, but radius and x remaining positive. Influencing the sine and tangent value of ?. However by the y value being negative it will not only affect sin ? but also tan ?= y/x, as a negative number divided by a positive results in a negative answer.

  1. Type II Portfolio - BMI

    This function was chosen because there is an obvious trend in the data that shows a curve. The sine function can easily be manipulated to fit the curve. The following equation shows how to manipulate the sine function: In this case all of the variables, which include a, b, c,

  2. Female BMI

    D controls the amount that the graph is shifted vertically. It is found using the equation shown below. Where max = maximum dependant variable value and min= minimum dependant value. These values were taken from the data table above and substituted into the equation, this is shown below.

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