• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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.

Extracts from this document...

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: image00.png

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.

...read more.

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.

image05.png

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)

...read more.

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        -  -

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. This portfolio is an investigation into how the median Body Mass Index of a ...

    graph follows a sinusoidal pattern when extrapolating data from the graph beyond 20 years of age. Based on common knowledge, girls are usually finished growing at 20 years of age - yet one can see that had the domain not been restricted in the sinusoidal function, the BMI would curve

  2. A logistic model

    15 16 17 18 19 20 Year 12 IB Mathematics HL Type II Portfolio: Creating a logistic model International School of Helsingborg - Christian Jorgensen Figure 5.2. Growth factor r=2.9. Graphical plot of the fish population of the hydroelectric project on an interval of 20 years using logistic function model {11}.

  1. Body Mass Index

    the general cosine function starts at x = 0 (which is the function's peak) shown in Figure 2. Looking back at Graph 2 we can notice that the greatest y-value is at x = 20. This tells us that the peak moved from x = 0 to x = 20.

  2. Maths BMI

    20.85 = 289a + 17(-10a) + c 20.85 = 289a - 170a + c 20.85 = 119a + c (5) - (4) 5.15 = 140a a= = 0.0368 (6) Substitute (6) into (1) b= -10a = -10 x 0.0368 = 0.368 Substitute (6)

  1. Virus Modelling

    26hrs 33mins 36secs for the immune response to begin for a person that that was infected with 10000 viral particles. 2. Using a spreadsheet, or otherwise, develop a model for the next phase of illness when the immune response has begun but no medications have yet been administered.

  2. math modelling

    So a good sailor would go out between 5.6-18.6. However now we have to find a best fit function for the original graph, this can be done using a graphical display calculator: So A=5.71 B=0.51 D=0.20 C=6.59 So the general rule is now 5.71 sin (0.51t + 0.2) + 6.59 Lets call this function, function star And if we

  1. While the general population may be 15% left handed, MENSA membership is populated to ...

    GPA 4.0-4.2 4.21-4.4 4.41-4.6 4.61-4.8 4.81-5.0 Total Dominant Writing Hand Left Hand ( ( ( ( Right Hand Total Expected Values (variables) Null Hypothesis: Students' GPA and dominant hand when writing are independent. Alternative Hypothesis: Students' GPA and dominant hand when writing are not independent.

  2. Creating a logistic model

    y = For r = 2.5, we have y = First, sorting out these logistic formulas into tabular form, we can represent this as: Initial Growth Rate (r) alogistic blogistic clogistic 1.5 6 0.6 60000 2 7 1.2 60000 2.3 7.4 1.56 60000 2.5 8 1.8 60000 From this table,

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work