Math Internal Assessment Gold Medal Heights
Gold Medal Heights
The heights achieved by gold medalists in the high jump have been recorded starting from the 1932 Olympics to the 1980 Olympics. The table below shows the Year in row 1 and the Height in centimeters in row 2
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 |
They were recorded to show a pattern year after year and to reveal a trend. The data graph below plots the height on the y-axis and the year on the x-axis.
Data Graph 1
Height (cm)
Height (cm)
Year
Year
In Data Graph 1 the data shown represents the height in cm achieved by gold medalists in accordance to the year in which the Olympic games were held. The Graph shows a gradual increase in height as the years increase. The parameters shown in this are the heights, which can be measured during each year to show the rise. The constraints of this task are finding a function to fit the data point shown in Data Graph 1. Some other constraints would be that there aren’t any outliers in the graph and it has been a pretty steady linear rise.
The type of function that models the behavior of the function is linear. This type of function models it because the points resemble a line rather than a curve. To represent the points plotted in Data Graph 1 a function is created. To start deciphering a function I started with the equation -
Y = mx + b
To show the slope of the line since the function is linear. For the first point the function would have to satisfy
197 = m (1932) + b
In order for the line to be steep the b value or y intercept will have to be low to give it a more upward positive slope.
Y = mx -1000
197 = m (1932) -1000
1197 = m (1932) m = 0.619
The final linear equation to satisfy some points would be
y = 0.62x – 1000
The graph below shoes the model linear function and the original data points to show their relationship.
The heights achieved by gold medalists in the high jump have been recorded starting from the 1932 Olympics to the 1980 Olympics. The table below shows the Year in row 1 and the Height in centimeters in row 2
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 |
They were recorded to show a pattern year after year and to reveal a trend. The data graph below plots the height on the y-axis and the year on the x-axis.
Data Graph 1
Height (cm)
Height (cm)
Year
Year
In Data Graph 1 the data shown represents the height in cm achieved by gold medalists in accordance to the year in which the Olympic games were held. The Graph shows a gradual increase in height as the years increase. The parameters shown in this are the heights, which can be measured during each year to show the rise. The constraints of this task are finding a function to fit the data point shown in Data Graph 1. Some other constraints would be that there aren’t any outliers in the graph and it has been a pretty steady linear rise.
The type of function that models the behavior of the function is linear. This type of function models it because the points resemble a line rather than a curve. To represent the points plotted in Data Graph 1 a function is created. To start deciphering a function I started with the equation -
Y = mx + b
To show the slope of the line since the function is linear. For the first point the function would have to satisfy
197 = m (1932) + b
In order for the line to be steep the b value or y intercept will have to be low to give it a more upward positive slope.
Y = mx -1000
197 = m (1932) -1000
1197 = m (1932) m = 0.619
The final linear equation to satisfy some points would be
y = 0.62x – 1000
The graph below shoes the model linear function and the original data points to show their relationship.