Graphical Analysis
• When we take data as scientist we need an efficient method for
picking out trends, and noticing relationships (correlations) between
the different parameters we are studying
• Graphs also help us predict the behavior of a physical system
• Being able to understand and interpret graphs is very important
• Extract abstract ideas about what you’re looking at
Comparison of 9 Week Grades
for Classes 9-12
Fertilizer Ingredients
95
90
85
Phosphorus
20%
80
75
70
65
Filler
60%
Potassium
10%
9th Grade
10th Grade
11th Grade
12th Grade
Classes
Car Distances Traveled During Race
Distance (meters)
9 Weeks Average
(%)
Nitrogen
10%
140
120
100
80
60
40
20
0
Chevy
Ford
Dodge
0
1
2
3
Time (seconds)
4
5
Nitrogen
Phosphorus
Potassium
Filler
Graphical Analysis
• what type of things can we conclude from this graph?
Distance (meters)
Car Distances Traveled During Race
140
120
100
80
60
40
20
0
Chevy
Ford
Dodge
0
1
2
3
4
5
Time (seconds)
• Which car went the fastest during any 1 second point of the race?
• Which car blew its engine?
• How far did the Ford travel between the 3rd second and the 5th second?
• What quantity does the slope of the line represent?
Graphical Analysis
• What makes a proper Graph?
– A coordinate system
• Origin, defined and labeled
• Data Points, instructions on how they are defined
• Axes, defined, labeled, which way is increasing, units used
axis labels must
have units on them
Q (t2, d2)
d2
axis
data points
d1
axis
P (t1, d1)
0
t1
origin
t2
arrow denotes the
direction that is
increasing values
Time (s)
Graphical Analysis
Q (x2, y2)
y2
Dy
y1
P (x1, y1)
0
x1
x2 Independent
Variable
•
•
Independent Variable: Experimenter Controls (temperature, weight, time)
Dependent Variable: Measurement (effect that changing the ind. variable had)
•
•
Interval (x-axis)
Interval (y-axis)
Dx = x2 - x1
Dy = y2 - y1
NO Relationship – Scatter Graph
Y
0
• Y Does NOT Depend Upon X
X
Proportional Relationship
Y
0
• As X increases, Y increases
• As X decreases, Y decreases
X
Y~X
Inversely Proportional Relationship
Y
0
• As X increases, Y decreases
• As X decreases, Y increases
X
Y ~ 1/X
Nonlinear (Quadratic or exponential)
Y
0
X
• As X increases Y increases much faster
• Y increases to a higher power (example area)
2
Area of Square (m )
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
Area of a square = Length of side x Length of side
Area = L
L
2
3
4
Area (m2)
1
1
2
4
3
9
4
16
5
25
6
36
7
49
8
64
9
81
10
100
2
L
1
Length (m)
5
6
7
8
Length of the Side of a Square (m)
9
10
Distance = (Speed)  (Time)
y = (m)
(x)
+ b
Q (t2, d2)
d2
Dd
d1
P (t1, d1)
0
t1
t2
Time (s)
• Time interval
Dt = t2 - t1
• Distance (y-axis) Dd = d2 - d1
• m = Slope of the line
rise y2  y1 d2  d1 Dd
slope 



 speed ! !
run
x2  x1 t2  t1
Dt
Density r
rwater = 1.0 gr/cm3
Lead
Mass (grams)
Ice
0
mass
m
Density 
r
volume
V
y  mx
Water
Volume (cm3)
(V ) r 
m
(V ) Vr  m
V
If something is going to float in water it’s density must be less
than the density of water (1.0 gr/cm3).
m  rV  slope  r
Density r
Mass (grams)
Water
Lead
Ice
Volume (cm3)
0
What if I were to ask you some questions about this graph.
A 10 cm3 volume of which substance would weigh the least? How would you go about
answering this question?
First you should ask yourself? What am I looking for?
m  rV
the substance with the lowest density will weigh the least!