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Numbers and Bones
Forensics Anthropology and Math
Read this and Watch this A Texan Tall Tale
If you are interested, also watch this episode: Dead Man’s Tales
The longest bone in the human body is located in the leg. This bone is called
the femur and can be used to estimate the height of an adult. Human
skeletons exhibit sexual dimorphism. As we build our mathematical models
will be more accurate if use one for each sex.
Height is a linear function of
several bone lengths: humerus,
radius, femur and tibia. This
relationship is of the form
y = mx + b.
Use information at this site to give
the location of each of the four
bones that have linear
relationships. Label the bones on
the skeleton.
We are first going to relate arm length to height. Measure from your elbow
to your wrist and record it on the board. Also get your height. Use the white
boards to make a good graph.
Calculate the slope and y-intercept. Try to write an equation.
We will use the TI 83 calculator to
find equations that relate height
and femur length. In order to do
this, we need to get some data.
Each of you should measure your own femur and your height. Record the
measurements on the data table on the board and in the data table below. Get the
data from each class member.
Boys
Height
Girls
Femur Length
Height
Femur Length
Turn calculator on. Press STAT, then hit ENTER. You should see lists. You need to
enter the data you have into the list. Enter girl data.
L1 will be the x-axis numbers, the independent variable. Since height depends on
the length of the femur. L1 will be femur lengths and L2 the total height.
After entering the data, hit STAT PLOT, and hit 1 or ENTER. Plot 1 should
be turned On, dots, Xlist:L1, Ylist:L2 . If Plot 1 is Off, put the cursor over On
using the arrow keys, and hit enter. Hit ZOOM, scroll down with the arrow
key to ZoomStat (option 9), and hit ENTER. You will see a scatter plot of
your graph on the screen.
To find the equation for this line, hit STAT, arrow across to CALC, scroll
down to LinReg(ax +b) and hit enter twice. It will give you an equation in the
form of y=ax+b. Below the equation will be the values for a, b and r. a is the
slope of the line, and b is the y-intercept. (r is the correlation coefficient.)
You might get an equation that said
y= 1.23 * x + 105.88 with r=0.65
This would mean
height = 1.23 * femur + 105.88.
In this example, a person with no femur would have a height of 105.88 cm.
The correlation coefficient for this line is .65, which is not great. The closer
r is to +1 or -1, the better the fit.
To draw this line on the graph, hit Y=, then VARS, scroll down to Statistics,
hit ENTER, scroll across to EQ, scroll down to RegEQ, and hit ENTER. Hit
GRAPH and you will see your scatter plot with the best fit line.
The accepted line for female height from femur length is: height = 1.95 *
femur + 72.85. To comapre this line to the one obtained from our sample, hit
Y=, scroll down to Y2=, and put in the equation. Hit GRAPH to see what the 2
lines look like.
Repeat the process for the boy data.
For Girls:
Equation =
R=
For Boys
Equation
R=
Scenario:
The Confederate submarine, the Hunley, sank on February 17, 1864, shortly
after an attack on the Union blockader U.S.S. Housatonic. The Hunley
earned its place in naval history for being the first submarine known to sink
another ship in war. But in doing so it perished itself, sinking mysteriously
almost immediately after it rammed the Housatonic.
(http://news.nationalgeographic.com/news/2001/10/1011_hunleytintype.html)
National Geographic has recovered remains believed to be the captain and
his first mate. The captain had a height of 6 ft. 2 inches. The first mate was
only 5 ft. 4 inches. The femurs from the remains have been sent to us. Use
your data to make the case. Could these bones be from the captian and his
mate? Why or why not? Support your answer. Show any math that you do!