The exact equation of the Gaussian function, which fits the data graph, is:
y =, where
A=-6,933
B= 5,510
C=8.846
D=22.15
It must be noted that it is highly possible the Gaussian function to be inappropriate if the data is for elder people. The biological development of the human body leads in most of the cases to changes in the weight, height and the mass amount, that if put in a data set and represented in graph those quantities would not look like the Gaussian graph. The Gaussian graph is symmetric and the age/BMI graph for elder people would not be symmetric. That is why, the Gaussian normal distribution is not appropriate for proceeding with the task.
The graph of an equation of highest power 5 fits well the graph, too.
The best way to show that the equation of highest power fits well to the graph of the data that is given is to draw the two graphs on what plot. The new graph looks like this:
The black line represents the equation y, where:
A = 18,81
B = -1,591
C = 0,2069
D = -0,007266
E =
F = 9,787
Before using this equation for a model, it is better first to test it. Using the graphical calculator I calculated the BMI of a 2-year-old girl. This is what I got:
The answer (16.398) is very close to real BMI of a 2-year-old girl, which is 16.40. This little testing gives me the courage to proceed with the task and to estimate the BMI of a 30-year-old woman in the USA using my model. The result is as follows:
The result looks relatively fine, because it is near to the quantity of the BMI of a 20-year-old woman and during that period of time (between 20 to 30-35 years) almost no radical changes happen in the female body. In Internet I found many BMI calculators and assuming that a woman, that is 30 years old, weights 58 kg and is 167 cm high, the BMI is estimated around 20.8. That could be assumed for another proof that my model could be used for relative estimating the Body Mass Index.
Also, I used the Internet to find BMI data for females from Brazil. I found the following information:
The graph, which represents this data, is:
My model does not perfectly fit this data, but using the same method, but with the different quantities one will develop another model, with different coefficients, which would fit this data better. Anyway, this model has limitations, because every race has different characteristics, including differences in weight, height, etc.
List of sources:
(March, 2009)
(March, 2009)
Owen, John. Haese, Robert. Haese, Sandra. Bruce, Mark. “Mathematics for the international student”, Haese and Harris publications
TI-84 Plus Silver Edition
Graphic Analysis 3.4 Demo Version
