# High Jump Gold Medal Heights Type 2 Maths Portfolio

by sarahvdpost (student)

Gold Medalist Heights

IB Mathematics SL Type 2 Portfolio

Sarah van der Post

2/4/12

Contents Page

Introduction                                                                        3

Considering Data -Heights of Olympic Games 1932 - 1980        3

Linear Model                                                                4

Natural Logarithm Model                                                7

Estimating and Predicting                                                8

Considering Additional Data - 1896 - 2008                                10

Cubic Model                                                                13

Gaussian Model                                                                        14

Conclusion                                                                        14

Introduction

The Olympic Games is a major event occurring every 4 years. International athletes come together to represent their country at a sport, first place winning a gold medal.  This portfolio aims to consider the trends of the winning men gold medalist’s high jump heights at various Olympic Games.

Considering Data - Heights of Olympic Games 1932 - 1980

The table below gives the height achieved by the men gold medalist’s high jumpers at various Olympic Games between 1932 and 1980.

Table 1: The winning heights of men’s high jumping in Olympic Games for years between 1932 and 1980. (Excluding 1940 and 1944)

Using excel, a graph has been produced to represent this data visually.

Graph 1: The winning men’s high jump heights in Olympic Games for years between 1932 and 1980. (Excluding 1940 and 1944)

The x-axis represents the year of the Olympic Games. This begins at 1932. The y-axis represents the Gold Medalists high jump height in centimeters.

Unfortunately, there are parameters to this graph. There were no Olympic Games in 1940 and 1944 due to the war. This meant that the data is not consistent as we are missing 2 years of Gold Medalist heights. The graph also only shows the heights of the 1932 to 1980 Olympic Games which is a small section of the overall Olympic Games data, beginning in 1986.

Linear Model

Graph 2: The winning heights of Olympic Games against years since 1932 (between 1932 and 1980)

In order to make calculations easier, I created a graph of height versus years since 1932 as seen in graph 2. When considering the trends and possible functions this graph models, I immediately thought that the function that models the behaviour of this graph is a linear function. This can be shown by the line of best fit in Graph 3 which is linear, where the line goes ...