Jeremiah Joseph

This Internal Assessment will investigate models of female BMI data. BMI is the measure of one’s weight to their height. To calculate a person’s BMI their weight is divided by the square of their height. Shown below is data for female BMI values in the US in 2000.

The data points shown above were graphed, the resulting graph is shown below.

The variables that were used in the graph above were age and BMI. The independent variable, age, was placed on the x axis. Age is the independent variable because it is constant. The dependant variable, BMI, was placed on the y axis. BMI is the dependant variable because is varies, dependant on the age.

It is clearly shown in the graph above that the BMI of females in the US in 200 can be modelled using the equation y= A sin (Bx-c) + D. This is because the graph is shown to have the same characteristics of a sin graph. In this equation A is the amplitude of the graph.

Where max = maximum dependent variable value and min = minimum dependent variable value. The maximum value obtained from the data is 21.65 whereas the minimum value is 15.20. These values were then substituted into the equation, this is shown below.



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In the sin equation aforementioned B is the measure of how much the graph is stretched horizontally. B is calculated using the equation shown below.

However, the period of this graph is unknown. To find the period of the graph the equation shown below must be used.

Where max = the maximum independent variable value and min = the minimum independent variable value. The maximum independent variable value = 20 and the minimum independent variable value = 5. These values were read of the data table, shown above, and then substituted into the equation, shown below.


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