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

Gold Medal Heights Maths Portfolio.

Extracts from this document...


Gold Medal Heights

The table below gives the data achieved by the gold medalists in the Olympic Games.

























Using this data, I will create a model to represent the relationship between the high jump results and the years they took place. However, the Olympic Games did not occur in 1940 and 1948 due to World War 2. The independent variable is time, so let x-years be time and the dependent variable is height, so let y-centimetres be height. The winning height is the dependent variable since each year resources, technology, competition and may more are altered. After plotting the data, the following scatterplot was obtained:

Figure1: Height vs. Year        Figure1.1: Window


Since x is in-terms of years, one may consider B.C as “negative” years.

 the domain is

. The range is in-terms of the height jumped by the medalist therefore, theoretically speaking it is impossible for humans to jump above a certain height because we have our limitations and we cannot jump below a height of 0.

 the range is

. The maximum height that can be jumped is set at 250cm because the highest achieved height by a human is 245cm by Javier Sotomayor.

...read more.


 Another function that could model these points is an exponential.

Figure 2: Exponential Function: Applying Reflections and Translations

When an exponential is reflected on the x and y-axis, the shape is similar to the plotted points. It is then translated d-units up, where d would represent the horizontal asymptote. Since e, Euler’s number, is a transcendental constant, I defined a as e and added –k to create a similar graph.


Since we know that the d-value is 250,



Since this function has three variables, three points must be chosen. To determine the first point, the first four data points are averaged, then the next four points are averaged to find the second point and finally, the last three data points are averaged to find the third point.

Point 1: image01.png


Point 2:image01.png


Point3: image01.png







Subtract equation 2 from 1




 into equation 3





Substitute equation 4 and

 into equation 1






46.469 into equation 4



Figure 3: Exponential and Cubic Modelsimage12.png

Both equations have their own limitations. The cubic function is not the best model because as


 and as


 the cubic function does not fit the range, but it fits the given data points well since the RMSE value for the cubic is 4.614.

...read more.


Works Cited

"High Jump World Records." Rob's Home of Sports, Fitness, Nutrition and Science. N.p., n.d. Web. 23 Feb. 2012. <http://www.topendsports.com/sport/athletics/record-high-jump.htm>.

"Logistic Equation -- from Wolfram MathWorld." Wolfram MathWorld: The Web's Most Extensive Mathematics Resource. N.p., n.d. Web. 22 Feb. 2012. <http://mathworld.wolfram.com/LogisticEquation.html>.

"Logistic function - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 22 Feb. 2012. <http://en.wikipedia.org/wiki/Logistic_function>.

"Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE)." Eumetcal. N.p., n.d. Web. 23 Feb. 2012. <http://www.eumetcal.org/resources/ukmeteocal/verification/www/english/msg/ver_cont_var/uos3/uos3_ko1.htm>.

"NOAA/ESRL Global Monitoring Division - THE NOAA ANNUAL GREENHOUSE GAS INDEX (AGGI)." NOAA Earth System Research Laboratory. N.p., n.d. Web. 24 Feb. 2012. <http://www.esrl.noaa.gov/gmd/aggi/>.

...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 ...

    Under this assumption, the value found is very reasonable. Also under this assumption, one can conclude based on this data that the median BMI of a woman who has reached both adult height and adult weight would be a value very close to the asymptote of the function - 22.9.

  2. Extended Essay- Math

    � �}�������h���)))��-/O2r K|!u(tm)� %>��/Vj+V��("VAdt��I�-�Y�֭;{��E�Ο?�""d��k ��Pn~�B^D"�9&�H�yK��(c))(r) Y� "#�V�Z�Ë�&M�6=|��9l�öm^���M�G(Z�5P�B�0!���K��0L�"#X��;�g�-t�m�.]�/^?�f�9&J-Z� >l! K�l� Ù1/2#' x� �4��N�<�ӬY3�R(tm)�3v��(r)]"���...pM���ÍC�&�>.�~Û¶m�x� ]|��b��...-U�>-�(�+l�Z$�a1/2Y� ЧO�^1/2zaÉ£#8�䷿�-Ì���Q~���-i��E� e"�$y1Z?� �k]Bd#a��daF'Hd�\""�� �"cG �m��ë�#� CKxpHFZ3/4�Z�q�Qd��Z�O�1/2A�d� (r)-��]�l$-�(� 8(D�bI0 i(c)�}��U�PAK�C"�J� G!x�'d���e��#�[n�e���Z*�B{���{��Ú��+(r)Z� (r)��*hQ �W�n�3/4]SWr-@�HHÎ4R�EQ���,d\�3/4C� ����Fb''7�z�*)�|�^v"�m�(c)q�&k�"!)��'9� �"sX8�z��ա(tm)�#ï¿½Ë @2�O����iii��Mb$r��+�h�(r)�d���á£"�:t���R $��$#�T�}} wd����B#�$#ʹ��p-�(tm)�'""4"Ùè¸$#@��I�O�z]�D /;�6Vj � �z�'���I\�0��7sH�'�;2�*'i�n$xlܸ�fB�&.Ң��wf ����3/4o i�Z8�/x�t��JM�w�mqIFn#�q{�� D6$��֬YY�'� �@Y�t O�2e�dff"g"Nr' +rWÖ¯_��1/2Zg�K` �ÎbB�� l�c+�L��"_�Jn�+�� �d$ j:���||1/4]�]xEtn�d�"�����H�q�]�#a N �H']gddT"VM'��È(tm)����*�(tm)��'�tR'L*�d�"�vd...�y���--��� ''N�Ĭ��ס �ѣ� |Z��� @2�F�0!��/��,`�����^ ''6����T�9A����V(�{������-@F�C����#N

  1. Math Portfolio Type II Gold Medal heights

    As one can see the break had a negative impact on the athlete's performance as the best achieved height fell by almost five centimetres in comparison to the previous games. This disrupts the general trend of improvement as one can clearly deduce from the following graph which uses the values

  2. Using regression analysis to solve a real time problem

    =3.67 Hence a driver of 25 years of age who maintained his vehicle 4 times and drove at an average speed of 100

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

    The table also tells us that approximately the value of 73.2% of the volume of the cuboid is equivalent to the wasted space. Maximum Cuboid Floor Area: We now investigate the maximum cuboid floor area to determine how much space we are able to use.

  2. High Jump Gold Medal 2012 maths investigation.

    After sketching the new model function using the original data using Geogebra. The gradient calculated by the software is represented by : y= 0.7456x+194.2535 Testing the software linear equation: y= 0.7456x+194.2535 Let x = 44, we expect y= 225. y= 0.7456 (44)+ 194.2535 y= 227.0599 There is a bit different from the actual data.

  1. A logistic model

    1.6u ?5 2 un?1 ? (?1? 10 )(un ) ? 1.6un {3} 3. Using the model, determine the fish population over the next 20 years and show these values using a line graph One can determine the population of the first 20 years just by knowing that u1=1?104 u2=1.5?104 .

  2. Math Portfolio: trigonometry investigation (circle trig)

    Positive x axis--- (+, 0) sin ?=y/r =+ cos ?=x/r=0 tan ?=y/x= 0 Negative x axis---(-,0) sin ?=y/r =- cos ?=x/r=0 tan ?=y/x= 0 Positive y axis---(0,+) sin ?=y/r =+ cos ?=x/r=0 tan ?=y/x= undefined Negative y axis---(0,-) sin ?=y/r =- cos ?=x/r=0 tan ?=y/x= undefined The value of x

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