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# GVPT 100 Lecture Notes - Lecture 15: Scatter Plot, Tarbosaurus, DaspletosaurusExam

Department
Government and Politics
Course Code
GVPT 100
Professor
Irwin Morris
Study Guide
Final

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BSCI 207 Spring, 2019
Homework #2: Scaling
11:59 P.M., Monday, February 18
Also on ELMS: some time on Sunday (February 17) or Monday (February 18) take
a short timed quiz on Scaling
You may work on this homework on your own or discuss it with others. If you work through
questions with others, be sure to turn in your own work, at the level at which you understand it.
Do not simply copy answers from or for someone else. Questions such as these may show up on
quizzes or exams, so be sure to work to understand how to arrive at the answers.
Note: Questions or statements in italics require a response from you.
Problem 1. Fish scaling
You have caught eight individuals of a particular fish species and measured the length, depth (vertical
height), and thickness (side-to-side distance) of each. For each fish, approximate total surface area and
volume of each fish were calculated, as shown in the table below.
LENGTH (cm)
THICKNESS (cm)
DEPTH (cm)
VOLUME (cm3)
AREA (cm2)
2
0.5
1
1
6
4
1
2
8
24
6
1.5
3
27
54
10
2.5
5
125
150
16
4
8
512
384
24
6
12
1728
864
48
12
24
13824
3456
60
15
30
27000
5400
Use Excel (or a similar program) to fit power functions (scaling equations, Y=axb) to these data (a
power function, which has the form y = axb, has a variable base raised to a fixed exponent). Exactly
how to do this will depend on your version of Excel. But the procedure will be something like this:
1. Select the two columns of numbers you wish to plot (e.g., depth and volume).
2. Click on the Charts tab [or Insert tab] & select Scatter plot [X Y scatter]
3. Select the resulting plot and click on the Chart Layout tab & Trendline subtab [Add chart
element, then Trendline]
4. Under Trendline Options, select Power [possibly under More trendline options] & under
Options (just to the left) [or under Format Trendline] click on “Display equation on chart”
and click OK.
The equation of the power function fitted to your data should be displayed on your graph.
1a) (1/4 pt) What is the value of b for depth vs. volume (note that “A versus B” tells you that A is
on the Y axis and B is on the X axis)? Paste your graph below.
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1b) (1/4 pt) What is the value of b for area vs. volume? Paste your graph below.
1c) (1/4 pt) What is the value of b for volume vs. area? Paste your graph below.
1d) (1/4 pt) What is the value of b for thickness vs. area? Paste your graph below.
1e) (1/4 pt) Do your fish appear to be growing isometrically or allometrically? Explain.
Problem 2. Dinosaur scaling
Theropod Dinosaur Species
Body Mass (kg)
Body Length (m)
Staurikosaurus pricei
19
2.08
Coelophysis bauri
15.3
2.68
Coelophysis rhodesiensis
13
2.15
Elaphrosaurus bambergi
210
6.2
Liliensternus liliensterni
127
5.15
Dilophosaurus wetherilli
283
6.03
Ceratosaurus nasicoris
524
5.69
Eustreptospondylus oxoniensis
218
4.63
Metriacanthosaurus? sp.
130
3.8
Allosaurus fragilis
1010
7.4
Allosaurus atrox
1320
7.9
Gorgosaurus libratus
700
5.8
Gorgosaurus libratus
2500
8.6
Daspletosaurus torosus
2300
9
Tarbosaurus bataar
760
5.8
Tarbosaurus bataar
2100
7.7
Tyrannosaurus rex
5700
10.6
Deinonychus antirrhopus
45
3.06
Deinonychus antirrhopus
73
3.43
Velociraptor mongoliensis
15
2.07
Ornithomimus edmontonicus
110
3.3
Ornithomimus brevitertius
144
3.66
Gallimimus bullatus
27
2.15
Gallimimus bullatus
440
6
The dinosaur data above were plotted in Excel, as shown below
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