The Relationship Between Human Height and Weight
- Roy Wright
- Functions, Power Functions
Below is a graph showing the heights and weights of a large group of people, including infants. Each dot represents a person.
Based on this, what is a normal weight for someone with a given height? In other words, if and represent height and "average" weight, can you find a formula for as a function of ? Try plotting some functions. For example, one not-very-good possibility is the linear function w(h) = 3.86h - 110.42, which you can plot by typing it into the input box at the bottom of the graph. For an extra challenge, see how well your best function can predict the weights of extraordinary people. For example, Robert Wadlow, the tallest officially recorded person in history, was 107 inches tall when he died, and weighed 439 pounds. Does your function match up with this? Mine does! Source data available at http://www.math.utah.edu/~korevaar/2270fall09/project2/htwts09.pdf