a clear strategy for exploring data from a single quantitative variable.
1.
Plot the data: make a graph
2. Look for overall pattern (shape, center, spread and unusual values)
3. Calculate a numerical summary to describe center and spread.
4. The new step:
Properties of a discrete random variable X:
1. 0 P(X) 1
2.
Let X = the number of shots I make in 3 attempts.
X
0
1
2
P(X)
0.1
0.25
0.5
3
Calculate the probability that
I make all 3 shots:
I make less than half of my shots
I make at least one shot
P(X = 3)
Entering data in a list: Stat: Edit
cfw_4, 9, 11, 13, 13, 15, 15, 16, 16, 16, 17, 17, 18, 19, 20, 20
Making histograms: Stat Plot: Plot 1 graph #3
-zoom: 9 zoomstat makes a nice window
-trace will show class boundaries and frequencies
-window: Xscl chang
1. How to confirm that the transformation fit the data to a straight
line:
a. Exponential models:
Residual Plots: after the LSR equation (L1, L3) has
been pasted into Y1, L4 = Y1(L1) and L5 = L3 L4.
Look at the scatterplot for L1 vs. L5(RESID).
Remember
Graphs
The horizontal axis should include the variable name and the
possible categories. The bars should have some space between
them to indicate they are freestanding and can be arranged in any
order.
The vertical axis can be frequency or relative freque
The z-score for a weight of 8 lb is: = .31.
This z-score is between 0 and 1 so we know at least 50% weigh less than 8
lb. We also know that at most 84% weigh less than 8 lb. Thus, between
50%-84% of babies weigh less than 8 lb.
*recall the information alr
Stemplots
The numbers to the left of the line are the stems (hundreds and tens
digits) and the numbers to the right of the line are the leafs (units
digits).
You must include a key (with units) and a label/title
Leaves should be single digits (no commas)
When should we stratify?
If you think there are groups within the population who may be
similar with regard to the question of interest, you should take an
appropriately sized simple random sample from each group.
In our example, we should anticipate that
LSR equations:
a. Exponential models:
Written log y = slope (x) + intercept
After an inverse transformation (see #5 part f or example
4.7 in the book when dealing with ln transformation) you
should end up with a y = abx
b. Power models:
Written log y =
EX 1
EX 2
EX 3
If
find
Substitution Theorem
If f(x) is a polynomial or a rational function, then
assuming f(c) is defined.
Ex 4
Ex 5
EX 6
Hint: rationalize the numerator.
EX 1
EX 2
Find the slope of y = -x2 + 3x when x = -1, 2, and 5.
Find the equation of the tangent line to y = 2 at x=1.
x
Geometrically finding the slope of a tangent line to a curve is exactly the same
as finding the instantaneous velocity for a moving ob
Parallel and Perpendicular Lines
Parallel lines have the same slope.
Perpendicular lines have negative reciprocal slopes.
EX4
a) Find the equation of the line parallel to 3x - 4y = 8 which passes through
the point (1,3).
b) Find the equation of the line p
Ex 5
Ex 6
Definition: Right and Left Hand Limits
means that when x approaches c from the right side of c,
then f(x) is near L.
means that when x approaches c from the left side of c,
then f(x) is near L.
Theorem A
iff
Determine these limits for this funct
There is only one line between any 2 points.
The slope of a line is:
The steepness of the line.
The vertical change over the horizontal change, denoted by m.
Given two points, (x1,y1), (x2,y2) in the Cartesian Plane,
m=
Examples of slope:
EX 1
a) Find the
Consider this function:
f(x)
3.25
7.25
7.2
3.1
7.05
3.05
7.01
3.001
7.001
3
?
2.00
6.99
2.95
6.95
2.9
6.9
2.8
What happens as we approach x = 3?
x
3.2
What happens at x = 3?
6.8
So we say as x approaches 3, f(x) approaches 7.
Algebraically we compute it t
EX 4
Find the volume of the largest right circular cylinder that can be
inscribed in a sphere of radius 8m.
EX 5
A right circular cylinder is to be designed to hold a liter of water.
Find the dimensions of such a cylinder which uses the least
amount of ma
It took me 6 hours to drive 400 miles. As I drove I wrote the mileage on the trip-o-meter each
half hour. Here is a graph of my trip.
t
(miles)
d
3
Distance
170
2.5 130
2.1 112
2
time (hrs)
What was my average velocity for the trip?
vav=
What was my avera
EX 1
An open box is made from a 12" by 18" rectangular piece of cardboard
by cutting equal squares from each corner and turning up the sides.
Find the volume of the largest box that can be made in this manner.
EX 2 A Norman window is constructed by adjoin
Ex 3
A child is flying a kite. If the kite is 90 ft above the child's hand level
and the wind is blowing it on a horizontal course at 5 ft/sec, how fast
is the child letting out the cord when 150 ft of cord is out? Assume
that the cord remains straight fr
EX 1
The Ladder Problem
A 20-ft ladder is leaning against a wall. The bottom of the ladder is sliding out
from the wall at the rate of 0.5 ft per sec.
How fast is the top of the ladder sliding down the wall?
How fast is the top of the ladder sliding down