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# Plot a graph for the BMI of different females of different ages in the US in year 2000 and analyse whether it is an accurate source of data.

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Introduction

Body Mass Index _        Maths Coursework

March 2008 _                By:  12M(2)

This maths coursework is based on Body Mass Index. This is a measure of ones body fat; it is calculated by taking one’s weight (kg) and dividing it by the square of one’s height (m). For this coursework, I have to plot a graph for the BMI of different females of different ages in the US in year 2000 and analyse whether it is an accurate source of data and how it can help me to find other BMI’s around the world.

Below is my graph showing the BMI of different females of different ages in the US in the year 2000:

As shown on the graph, the ‘x’ values are the age of the females and the ‘y’ values are their body mass index. The age is measured in Years.

When modelling this data, the initial impression is to think that is was an f(x)= x2 graph. However once you notice that it is not a mere parabola but a wave due to the curve that levels off (shown on graph) we can assume it is a periodic function such as a cosine or sine graph. Even though you can use a cosine or a sine graph, I decided to use a cosine graph, as I am more familiar with this type of graph.

Middle

There are various differences in the two models. This is expected, as they are two different functions. From ages 0-4 the cosine model (blue line) is very inaccurate and the cubic function is very accurate as it almost touches the points. They are both very accurate when a person is 13 years old as they both touch the point at (13, 18.7) and each other. Overall, it seems as though the cubic graph is much more accurate as it seem to touch many more of the points and also smoothly touches the trough of the curve.

As shown above, extending the x axis to 30 can show a possible trend. If you look at both the cubic and cosine graph you can see that they both decrease. Hence, we can say that a person of 30 years old will have a lower BMI than a person of 20.  However, the rate at which the BMI falls is much slower in a cosine graph than in a cubic graph as it is much steeper and has different gradients. If you substitute the x value of 30 in the equations we can find and prediction for each of the graphs. According to the cosine graph, substituting 30 into the equation (f(x)= 3.2cos(11(30)-230) + 18.5) equals 17.9 (to 3 s.f.). Thus according to the cosine graph, a woman aged 30 years old will have a BMI of 17.9. However, if we substitute 30 in the cubic equation we will find a completely different answer: (y=-0.004075(30)³+0.1536(30)

Conclusion

There are various limitations to my model. Firstly, there are much more results for my Australian data. This means that it is much more accurate. However, my American data has a wider age range, this makes it easier to see a trend than with my Australian data. Furthermore, the dates are different. The BMI was recorded in America in 2000, while the BMI in Australia was taken in 2002. Hence, Australia has much more recent results and are much more up to date. This means that this is just a vague comparison and is incorrect as it is not a fair test because many of the variables are changed.

In conclusion, the analysis of body mass index is very ambiguous and is a complicated procedure.

Bibliography:

1. Autograph Software
2. http://www.health.gov.au/internet/wcms/publishing.nsf/Content/health-pubhlth-strateg-hlthwt-obesity.htm

Indus tutorials         March, 2008        -  -

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