# Body Mass Index

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Introduction

Body Mass Index Maths Coursework by Warren Hui

Body Mass Index Math Coursework

By Warren Hui

Body Mass Index Math Coursework

By Warren Hui

Introduction

This piece of coursework will be based on data of the median BMI for females of different ages in the US in the year 2000. It will be a modeling task and I will model the data using different functions.

BMI or Body Mass Index is a measurement of someone’s height in relation to their weight; this standardized ratio is usually used to determine someone’s health. BMI can be calculated by dividing your weight (in kilograms) by the square of your height (in meters).

- Using technology, plot the data points on a graph. Define all variables used and state any parameters clearly

The first thing I did was input the data into the x column. This is because age is the constant. Then I named the column ‘Age’ to make sure the x axis has a title.

The graph is plotted but all the points are connected and this makes the data become inaccurate, so I right click and chose ‘Graph Options’ and uncheck the Connect Points box.The dependent variable in this graph is the BMI which is dependent on the Age (independent variable). The parameter a constant in the equation of a curve that can be varied to yield a family of similar curves. The black dots show the median BMI in respect to the age.

Middle

- Use technology to find another function that models the data. On a new set of axes, draw your model functions and the function you found using technology. Comment on any differences.

Before I chose another function that models the data I had two equations in mind. Either the Cubic, Quartic or Quintric. In order to see which equation models my graph more accurately I would look at the RMSE

Cubic graph

The RMSE is 0.0786418. This is already very accurate.

Quartic graph

The RMSE is 0.04564, this is very accurate and smaller then the Cubic graph’s RMSE.

Quintric

RMSE: 0.04725, this number is bigger then the Quartic graph but smaller then the Cubic graph, so I chose to use Quartic

Quartic is the most accurate graph, therefore I will use it for the next question. Some possible limitations in using the Quartic function is that it is only a best fit for age 2-20. If new data was presented, or we used this function to try and predict data outside of the data provided there may be errors. This is because the quartic function is only best fit for the current data provided, therefore we cannot solely rely on the quartic function for predicting values outside of the data provided.

If we zoom out, we will see the quartic graph dropping a lot after age 30.

Conclusion

Even with this weakness in the data, I chose to use the Gaussian graph of the Bahrani women to compare with the original data graph because the RMSE for the Gaussian graph is the lowest.

Gaussian graph values:

A: 7.102

B: 17.46

C: 5.595

D: 15.04

The Gaussian graph compared with the original data graph

RMSE: 0.795802

Conclusion

From looking at all these functions modeled from the Bahrani girl’s graph, we can tell it fits with the original BMI data for women.

After completing the task, I have found a flaw using the Gaussian function. Since it is named the ‘bell shape’ graph, after age 30 it drops back down to a straight line. This is extremely unreasonable, as women’s BMI will not drop significantly after age 20 to 15.1, which is equivalent to the BMI of a 3 year old.

However due to the limited data provided for the Bahraini girl, and I’ve tried every single function, there is no solution to that issue. However this can be solved by gaining more data on Bahrani women from age 19-30.

However from accuracy point of view a RMSE of 0.795802 when comparing the Gaussian graph and the original BMI of women shows the similarities. Based on my findings, the function that fits best is Gaussian, even though when it drops down to a constant of 15.1 it is still more reasonable then the Quartic graph which drops eventually to a 14.3. Dropping to 15.1 on the Gaussian graph and staying at that is reasonable if the BMI was slightly higher, this is because after age 30, a women’s BMI should not fluctuate much, if at all.

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

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