- Level: International Baccalaureate
- Subject: Maths
- Word count: 2165
The Sky Is the Limit Portfolio. In this assignment I will be building a model for the relationship between the winning heights in mens high jump and the years that they took place.
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Introduction
The Sky is the Limit
In this assignment I will be building a model for the relationship between the winning heights in men’s high jump and the years that they took place.
The high jump event in the Olympics is a track and field athletics event. It is held every four years in the summer Olympics. In the event competitors must jump over a horizontal bar that is placed at various heights. The high jump has existed for centuries now and was popular in ancient Greece. Javier Sotomayor holds the current world record for men’s high jump with a jump of 245 centimetres.
The table below gives the height (in centimetres) achieved by the gold medalists at various Olympic Games. Note: the Olympics were not held in 1940 and 1944 due to World War II.
The independent variable is time; so let t years be the time. The dependant variable is height; so let h centimeters be the height. It is important to note that height cannot be negative as it is physically impossible to have a jump that is below 0 centimetres.
A constraint of plotting this data is that there are two missing points for the years 1940 and 1944, as there were no Olympics during these years.
Middle
From looking at the graph above it seems as though a better fit for this function would be if the first point started at (1948, 198). This is partly because the Olympics were not held during World War II, which creates a gap in data. This war also meant that the athletes were unable to train so this is a reasonable assumption of why the two points after the war are almost identical to the points before the war. For this reasoning it would be acceptable to start the function at the point (1948, 198). To find the new equation for this function I used trial and error once again and found that the most suitable equation was:
The model above fits the points better, however it ignores the first two data points. In both of the square root models created there will be outlier points, but in the second one there are less for the data given. For the predicted reason stated earlier, both of the square root functions that I created are acceptable to use. Also, the second model for the square root function is likely to be more accurate in predicting the winning heights for the future because it fits the data very well.
Conclusion
My models created were effective for visualizing the data and also to predict winning heights for the future. When creating models like the functions in this assignment it is important to think logically and realistically. For example, simple things in this assignment were to realize that the height cannot be negative or that there will always be some outlier points because the winning heights will not increase consistently. The logical portion of creating models is perhaps even more important. If both of these aspects are thought about carefully than effective models will be created.
This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.
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