Mid Term Exam
Review Part 2
If you could predict the
future, what would you do?
Hurricane Katrina
Scatter Plots
(used to display a trend)
An effective way to hunt
for patterns or trends is
to display the data as a
scatter plot.
The difference between
independent and dependent
will be determined by insight.
Typically, the IV comes first
Ex pay vs hours worked
Pay: DV and Hours: IV
Outlier
An outlier is a point separated from
the main body of the data.
Todays Lab…..
Distance Vs Height
Distance (m)
(dependent)
4
3
2
1
10
20
30 40
50
60
70
80
90
100
Ramp Height (cm)
(independent)
Direct Variation
Consider working at McDonald’s
You get paid $8.00 per hour
Hours
Pay ($)
1X 8
8
2X8
3X8
16
10 X 8
80
24
In Direct Variation,
one variable equals
a fixed multiple of
the other.
Hours
Pay ($)
1X 8
8
2X8
3X8
16
10 X 8
80
24
This multiple is called
the constant of variation (k)
Hours
Pay ($)
1X 8
8
2X8
3X8
16
10 X 8
80
24
The formula:
P =8h
P
Pay vs Hours
48
40
32
24
16
8
0
0 1
2
3
H
4
5
6
How much would you get paid for 3.5 hours?
P = 8 X 3.5
= 28
P
48
40
32
28
24
16
8
0
0 1
2
3.5
3
4
H
5
6
How much would you get paid
for 7 hours?
P=8X7
= 56
P56
48
40
32
24
16
8
0
0 1
2
3
H
4
5
6
7
Partial Variation
Consider working at East Side Mario’s
You get paid $8.00 per hour.
You also get paid a $20.00 shift
gratuity.
Hours
Pay ($)
1X 8
8 + 20 = 28
2X8
3X8
16 + 20 = 36
10 X 8
24 + 20 = 44
80 + 20 = 100
In Partial Variation, one variable
equals a fixed multiple of the
other, plus a constant value.
Written as an equation
Variable
part
Fixed
part
P = 8h + 20
P
Pay vs Hours
60
50
40
30
20
10
0
0 1
2
3
H
4
5
6
What if we draw 2 lines on the
same graph?
We create what is called a linear
system.
P
48
40
32
24
16
8
0
0 1
2
3
H
4
5
6
Engineers have created a
mathematical measure for the
steepness of a line
Slope: The measure of a
line’s steepness
Steepness?
Direction?
Straight?
Distance
Time
Slope =
Rise
Run
Rise
Run
Step Count Technique
Count the number of steps
going from left to right.
2
5
5
m=
2
4
2
2
m=
4
1
m=
2
-5
-5
m=
2
2
First Differences
Be sure to copy down all the text in black.
All the colored text is just for reading and
reflecting
Time
Distance
First
Differences
0
0
1
2
2–0=2
2
4
4–2=2
3
6
6–4=2
4
8
8–6=2
Imagine the snake at
2 m / second
Add a First
Differences
Column to
your chart
When the
FDs are the
same, the
relationship
is linear
In summary
FDs are the same, then linear
FDs are different, then non-linear
Use a TOVs with a FD column
to determine if the following
relationship is linear or not.
See sheet