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

# 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.

Extracts from this document...

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 was the most suitable.     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.

## 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

# Related International Baccalaureate Maths essays

1. ## A logistic model

?2.6 ?10?5 u ? 2.56 {6} n n Using equations {1} and {2}, one can find the equation for un+1: un?1 ? run r ? ?2.6 ?10?5 u ? 2.56 n n ? u ? (?2.6 ?10?5 u ? 2.56)u n?1 n n ?

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

cuboid, we test to see how our independent variable (the maximum height of the roof) affects our dependant variable (the cuboid). Using the same methodology in Method 3, the following table was constructed and calculated using the GDC. The maximum and minimum height of the roof was chosen.

1. ## Stopping distances portfolio. In this task, we may develop individual functions that model the ...

We model only a quadratic function here, as it is justified from the last graph (speed vs. braking distance). This graph is very similar to the one of the breaking distance. It also makes sense seeing that the faster the car will be going, the time it will take to stop will increase more rapidly than the distance it takes.

2. ## Function that best models the population of China. Some of the functions that ...

I will substitute and then solve for b: Sub b into New equation is There are also some other values I got for both a and b when I did it with the same method but with different values of x and y: y = 657.5 x = 1965 y

1. ## This essay will examine theoretical and experimental probability in relation to the Korean card ...

but has one 10, third one is when player 2 does not have ?and 10 but has 9 and last one when player 2 does not have ?, 10 and 9. Graph 3. Tree Diagram of Ddang-8 P(1) = (2/20)

2. ## IB Mathematics Portfolio - Modeling the amount of a drug in the bloodstream

I assume that the left over drug would start building up in amounts in the body. Example, after 6 hours, there is 4 microgram of drug left in the bloodstream.

1. ## High Jump Gold Medal 2012 maths investigation.

I also decided to use the function to predict the result in 1984 and 2016 1932 - 1984 = 52 years y= 217.9381 + 19.2462 sin (0.054x- 1.758) y= 234.63 cm 1932- 2016 = 84 years y= 217.9381 + 19.2462 sin (0.054x- 1.758)

2. ## Modelling Probabilities on games of tennis

We can then subtract such cases to come up with the number of games of exactly y points. y = 4: 2 = 2 y = 5: 2 ? 2 = 8 y = 6: 2 ? 2 ? 8 = 20 y = 7: 2 ? 2 ? 8 • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to 