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High Jump Gold Medal 2012 maths investigation.

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Introduction

Gold Medal Heights

In this task I will develop a function that best fit the data points in the graph, which will be plotted based on the table below showing the different gold medal heights. 


Year

1932

1936

1948

1952

1956

1960

1964

1968

1972

1976

1980

Height (cm)

197

203

198

204

212

216

218

224

223

225

236

Number of years start from 1932

Height (cm)

X-axis

Y-axis

0

197

4

203

16

198

20

204

24

212

28

216

32

218

36

224

40

223

44

225

50

236

Note: There are no data of 1940 and 1944


For all the graphs in this table, the y- axis will be represent the height in cm and the x-axis will be the year when the height was obtained.

The graph below shows the relationship between the years and the heights obtained between the years of 1932 and 1980:

image00.png

The further explanation for the missing data in 1940 and 1944 was due to World War II.  Although the data does not tell us the reason why the height increased in 1932 and 1936 and drop down abruptly in 1948, we can assume that the World War II had affected athletics health critically.

...read more.

Middle

1932-1940 = 8 years

y= 217.9381 + 19.2462 sin (0.054x- 1.758)

x= 8

  • y =199.27 cm

1932-1944= 12 years

y= 217.9381 + 19.2462 sin (0.054x- 1.758)

x= 12

     => y = 200.7 cm

The answer would be mathematical reasonable increasing if we assume the data follows sine equation. The data are still in human range that the athletic can perform, however it is hard to say that they are 100% correct since we only rely on technology.

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)

y=224.8 cm

The answer are mathematical correct. However, in reality we do not know whether the data will truly describe the result since we only the data up to 1980.

Data table from 1896 – 2008:        

Numbers of year

Actual height/cm

0

190

8

180

12

191

16

193

24

193

32

194

36

197

40

203

52

198

56

204

60

212

64

216

68

218

72

224

76

223

80

225

84

236

88

235

92

238

96

234

100

239

104

235

108

236

112

236

The graph below represents the data from 1896 to 2008 :

image04.png

...read more.

Conclusion

an class="c11">227.3

76

197.6

80

190.2

84

216.0

223.1

237.3

194.1

223.1

192.5

194.1

220.7

192.5

237.6

220.7

218.6

237.6

Different between the actual data and data calculated by using

y= 212.9337 + 24.6777 sin (0.0324x- 1.9601)

y= 212.9337 + 24.6777 sin (0.0324x- 1.9601)

Actual height

Difference

190.1

190

0.1

227.5

180

47.5

236.1

191

45.1

210.9

193

17.9

201.8

193

8.8

233.9

194

39.9

206.1

197

9.1

188.3

203

-14.7

231.0

198

33.0

201.6

204

-2.4

188.8

212

-23.2

211.1

216

-4.9

236.1

218

18.1

227.3

224

3.3

197.6

223

-25.4

190.2

225

-34.8

216.0

236

-20.0

237.3

235

2.3

223.1

238

-14.9

194.1

234

-39.9

192.5

239

-46.5

220.7

235

-14.3

237.6

236

1.6

218.6

236

-17.4

After comparing the data between the actual provided height and the new best-fit model when we have addition data, it seems to be likely describing the nature of the data. However, the function does not fit in most of the data. Moreover, a better function should be investigated to make sure it goes through all the data point. However, due to the limit knowledge at the moment when I only know about linear, exponential, sine, logistic functions, it prevents me from going further to develop a more advance function which fit all the data points. Although the two functions have their R-values near to 1, especially sine function, it does not go through all the data point.

...read more.

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