# The aim of the assignment is to examine the gold medalist heights for the high jump in order to find the best fitting equation to represent the heights obtained by the gold medalists from the years 1932 through until 1980.

SL Mathematics: Type II Internal Assessment

Gold Medal High Jump

High jump is an Olympic event in which the goal is to jump over a bar as high as possible. The sport changed drastically during the years that are being examined. Many factors affected the growth of this sport such as: the change and improvement in technique (the invention of the Fosbury Flop for example), World War Two, the introduction of body building in sports and the increased awareness and knowledge of human health.

The aim of the assignment is to examine the gold medalist heights for the high jump in order to find the best fitting equation to represent the heights obtained by the gold medalists from the years 1932 through until 1980. I will look into the correlation between the year and the Gold medalist’s high jump height

The following table shows the height recorded by the gold medalists at the Olympic games from 1932 – 1980. The years 1940 and 1944 have been omitted due to the Olympic games being cancelled those years as a result of World War Two.

Note: Variable x corresponds with year and variable y corresponds with height. This will be relevant in future equations.

There is no obvious trend that the points plotted on the Raw Data graph indicate, however it appears that there are two turning points. This could perhaps be an anomaly because of World War Two. I created a cubic function for my first model, and therefore must use a cubic equation: y = ax3 + bx2 + cx + d.

Judging from the results shown in the raw data, it appears that there is an increase from 1932 through to 1936. There is then a decrease in height at (1948, 198), followed by a relatively steady increase. These changes in heights illustrate two distinct turning points (at 1936, 203) and at (1948, 198). A cubic function is effective for this set of data specifically because of the concave up and down shape, although if it were for Gold Medal High Jump results in the future, a logarithmic model as it illustrates humans infinitely increasing ability. However, the years provided were focused upon. The points used for illustration are shown in bold.

Table # 1: Raw Data

The Analytical Model

I decided to choose the points (1932, 197) and (1980, 236) so that the beginning and end points will be clear. I chose (1952, 204) and (1980, 236) because they are equidistant from the beginning of the graph and the end of the graph, respectively.

Using the results I obtained using PLYSMLT2, I input my four points in order to obtain my four variables (A, B, C, D).

y = ax3 + bx2+ cx + d

197 = a (1932)3 + b (1932)2 + c (1932) + ...