Student Investigation 6.1
Predicting Height from the Length of Limb Bones
BackgroundThe formation of bone by the activity of osteoblasts and the addition of minerals and salts is known as the process of ossification. This process begins in the fetus before birth and continues to some extent until about the age of 25. Although every person's bone development schedule is unique to that individual (just as the schedule at which they begin to walk or when they begin to talk is very individual and unique), a general timetable, Table 1, has been developed that indicates the various ages at which certain bones for the "average" person will complete ossification.
As you can see, during your high school years, the bones of the upper limbs and shoulder area are completing ossification. Also, by the ages of about 18 to 23, the bones of the lower limbs have been fully formed. In the average person, once ossification of the upper and lower limbs is complete, the size of the two major arm bones (the humerus and the radius) as well as the size of the two major leg bones (the femur and the tibia) have grown to a length that is proportional to the person's height. In fact, so precise is the relationship between these various bones and height that anthropologists and forensic scientists, with one dried bone as a clue, can closely estimate its owner's former living height.
For your information, an anthropologist is a person involved in studying humans in relation to their physical character, distribution, origin, racial background, social structure, and culture. Anthropologists are often involved with digging for and finding the remains of people who lived years and years ago. Certain kinds of remains, such as bones, can serve to provide information about the physical characteristics of these ancient people. A forensic scientist is a person who was trained to take evidence from crime scenes and determine from that evidence who may have been involved in the crime. Both of these groups know that certain bones serve as excellent sources of information to determine a person's height. Such a determination is accomplished using a set of standard equations that contain the scientific information gathered from hundreds of studies. For instance, if a 17.9 inch femur is found, this value is inserted into the following equation:
Height in inches = (1.880 x femur length) + 32.010and the result is that the femur belonged to a person who had a height of five and a half feet, assuming this person was a male. If the person were a female, a different equation must be used:
Height in inches = (1.945 x femur length ) + 28.679and the result is that the femur belonged to a woman whose height was about five feet, four inches. Now, let's look at the two equations above.
Both follow a very important form that is equivalent to the equation of a line:
Any equation of the form y = mx + b has a graph that is a straight line. The y-intercept, b, is the y value when x = 0. Thus, the point (O,b) lies on the graph of the straight line. The number m is called the slope, and it is an indication of how the line slants. The greater the slope, the steeper the line slants upward, from left to right. If the slope is negative, the line slants downward from left to right (Figure 11).
The fact that the length of the limb bones and its associated height is described by a linear equation such as this means that if you were tograph, for a group of different height individuals, the length of a particular limb bone along the x-axis and their height along the y-axis, the points on the graph should fall generally along a straight line. However, the slope of each line will always be positive.
You must be wondering why we have gone into detail about determining the equation of a line. Well, for this exercise, you will be doing just that. But that's not all. A small competition between groups is involved here! Let's begin.
Everyone should read all of the steps before beginning.
Step 1Break into groups based on your teacher's instruction. For each person in the group, two measurements will be taken:
Step 2The data for each person should include the two measurements. Graph the data with the length of the humerus along the x-axis and the subject's height along the y-axis. Once all of the data is graphed, draw a straight line along the data points and extend it so that your line intersects with the y-axis. This point will be the y-intercept. Next determine the slope of the line based on the model in Figure 11. Finally, determine the equation of your line.
Step 3After each group has completed their data collection and has determined the equation for their lines, it will be time to determine which group came up with the most accurate equation. Select two or three "new" people from another group and switch them with two or three members of your own group. Select people of different heights. Each group will then measure the length of the humerus bone for each of the "new" persons and determine their height using two methods:
Step 4Based on your experiences, each group must answer the following questions.
Dry BonesAdapted from the original African American Spiritual
The foot bone connected to the leg bone,