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

models and graphs relating the Body Mass Index for females to their ages in the US in the year 2000

Extracts from this document...

Introduction

Anh Nhu Vu

IB

Mathemathics Standard Level 2008

Maths Coursework

This coursework will explore models and graphs relating the Body Mass Index for females to their ages in the US in the year 2000. The ages and the corresponding BMI numbers are variables and as we generate the function that models the behaviour of the graph later on, the parameters are the values of a, b, c and d in the formula of the function.

When the data points are plotted on a graph, it is interesting to see what kind of graph these points are forming.

image00.png

The graph BMI appears to resemble the graph of a trigonometric function. If we base on the function y=sinx to develop our model function, the type of function that models the behaviour of the graph is:

y1=a×sin [b(x+c)] +d

These are the reasons why I chose this type of function:

Primarily, the shape of the graph resembles that of the graph of the function y=sinx.

However, in comparison to the graph of the function y=sinx, the data points of the graph BMI indicates that the processes of transformation have been done:

_Vertical and horizontal stretch (the scales are represented by a and b)

_Vertical and horizontal translation (the scales are represented by c and d)

...read more.

Middle

20-7.5=12.5 places and it is shifted vertically upward: 21.65-3.225=18.425 places.

 Therefore we can fully develop our model function:

y1=3.225× sin [image03.png(x-12.5)] +18.425

The graph of this function is presented below:

image04.png

Having developed an equation that is deduced to fit the original graph BMI, it is interesting to see how my model graph fits the points on the original graph BMI as well as to see the differences.

image05.png

There are clear slight differences between the graph Y1 and the graph BMI. We can see that the graph Y1 is an approximation of the original data. The table below shows how the values of y corresponding with the same values of x vary between the two graphs.

x

y value (BMI)

y value  (Y1)

2

16.4

15.815

3

15.7

15.487

4

15.3

15.27

5

15.2

15.2

6

15.21

15.27

7

15.4

15.478

8

15.8

15.815

9

16.3

16.267

10

16.8

16.812

11

17.5

17.428

12

18.18

18.087

13

18.7

18.762

14

19.36

19.421

15

19.88

20.037

16

20.4

20.582

17

20.85

21.034

18

21.22

21.371

19

21.60

21.579

20

21.65

21.65

These differences can

...read more.

Conclusion

Having said that, it is interesting to see some other BMI-for-age percentiles graphs that look similar to our original data BMI.

This is the data on the BMI related to ages for girls from the ages of 2 to 20 years.

SOURCE: Developed by the National Center for Health Statistics in collaboration with the National Center for Chronic Disease Prevention and Health Promotion (2000).

image11.png

If we go through the process of transformation again, we could also develop functions that model the behaviours of these graphs. However, it is unlikely that we can use the graph to estimate further feature of the data.

In conclusion, mathematical models in some cases can hardly be used to explore the natural tendency of certain real situations; in this case the BMI data. We can generate functions that model some behaviour of some data, but the actual data will not follow the rule of mathematical graphs. This fact is most obvious in the case of the BMI data of the females in Lebanon, in which it is very difficult to develop a function that fits the data well.

Bibliography:

http://www.emro.who.int/Publications/EMHJ/1302/article21.htm

http://www.health.vic.gov.au/childhealthrecord/growth_details/chart_girls4.htm

...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 ...

    to the same domain and range as the domain and range on the scatterplot, the graph of both the data and the function together is as follows: Comparing the two graphs, one can see that where BMI = 18.4 in the function is around 0.400 years off from the corresponding point on the scatterplot where BMI = 18.4.

  2. Math IA type 2. In this task I will be investigating Probabilities and investigating ...

    Having made all the required models, I will now analyze them. Some of the benefits of such types of model might include that it could provide mathematical evidence and guidance for gamblers and they could make educated bets on the player that is most likely to win.

  1. A logistic model

    Growth factor r=2.0. Graphical plot of the fish population of the hydroelectric project on an interval of 20 years using logistic function model {5}. 8 IB Mathematics HL Type II Portfolio: Creating a logistic model International School of Helsingborg - Christian Jorgensen Table 4.2.

  2. Stellar Numbers. In this task geometric shapes which lead to special numbers ...

    43 Adding 7x3 to previous 7S4 71 Adding 7x4 to previous 7S5 106 Adding 7x5 to previous 7S6 148 Adding 7x6 to previous Once again, another pattern was observed as the stage numbers developed. This time, the link that was found was that the number of dots in the next

  1. Function Transformation Investigation

    This time, we will investigate reversing the sign of the input or output. To begin with here is a series of graphs: The transformation clearly appears on these graphs. We can directly conclude that: * Reversing the sign of the input reflects the graph's image in the y axis.

  2. Maths BMI

    15.7 = a(3)2 + b(3)2 + c 15.7 = 9a + 3b + c Using another point on the graph, I let the x value be 17 and therefore, the y value is 20.85 (3) 20.85 = a(17)2 + b(17)2 + c 20.85 = 289a + 17b + c Now

  1. Body Mass Index

    However, in the data provided, the period is incomplete so it becomes sin x = 2?b, where I have to find b. From looking at the graph, I assume the graph is half the period, so ill calculate the value of half the period which is the maximum (20)

  2. Investigating the Graphs of Sine Function.

    This conjecture can also be expressed in terms of characteristics of the wave form. A represents the wave's amplitude, as it has been said before, but does not affect the wave's period as it remains constant in all curves. This can be noticed in all graphs shown before as it

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