Quantitative vs Qualitative

1
Quantitative vs Qualitative
Quantitative
Qualitative
Measures quantity and can be described
numerically.
Describes a category and cannot be measured
numerically.
Age, Weight, Height, Time
Hair Color, Zip Code, Favorite Color
Classify each data set as quantitative or
qualitative.
Number of students in a class
Quantitative
Phone numbers of students
Qualitative
That was easy
Football jersey numbers
Qualitative
Height of basketball players
Quantitative
2
Types of Data
Asi De Facil
Univariate
Bivariate
Data that uses two variables
Data that uses only one variable.
Lengths and widths of a rectangle
Weights of football players
Population
The entire group that you want information about.
Sample
The part of the group that is actually surveyed.
Sampling Methods
Stratified
Random
Systematic


Survey a population at random
Select a number n at random and survey every nth
person
Separate a population into smaller groups, then
survey each group
Survey people whose names are drawn out of a hat
Survey every 5th person that walks by
Separate a high school by grade level, then
survey a random sample from each grade
3
Determining Bias in a Sample
The question is biased because the word exciting
makes action films sound more interesting.
A survey question has bias when it contains
assumptions that may or may not be true.
You ask local residents, Do you prefer exciting
action movies or boring documentaries?
The question is not biased .
You ask local residents, Do you prefer action
movies or documentaries?
The location where a survey is conducted can also
cause a sample to be biased.
You ask people leaving Modells if they prefer to
watch sports or local news on TV.
The question is biased because people shopping at
Modells will tend to be sports fans.
You ask people leaving Target if they prefer to
watch sports or local news on TV.
The question is not biased .
4
Multiplication Counting Principle
In your closet you have 3 pair of pants, 7
shirts, and 2 sweaters. How many different
possible outfits can you wear using one pair of
pants, one shirt, and one sweater.
There are 42 possible outfits.
The cafeteria offers 4 main courses, 3
vegetables, 5 desserts, and 6 drinks. How many
possible meals can you have containing one main
course, one vegetable, one dessert, and one
drink?
There are 360 possible meals.
Asi De Facil
5
Evaluating Factorials
A factorial is the product of all positive
integers less than or equal to a whole number.
Does that say FIVE!!!?
five factorial
three factorial
Noit says 5 factorial.
six factorial
Asi de Facil
6
Working with Factorials
How many different batting order can you have
with 9 baseball players?
Holy cow! Thats a lot of different
possibilities.
That was easy
A swimming pool has 8 lanes. In how many ways
can 8 swimmers be assigned lanes for a race?
7
Permutations
Thats a factorial.
There are 10 runners in a race. In how many
different ways can they be assigned a running
lane?
There are 10 runners in a race. How many
arrangements of 1st, 2nd, and 3rd are there?
Thats a permutation.
Method 1
Method 2
10P3
Holy Schnikies! Its the same answer.
Asi de Facil
8
Combinations Permutations
In a permutation order is important. In a
combination order does not matter.
Mrs. Spankawitcz has 18 students in her math
class. How many different arrangements are there
for her to pick 4 students at random to be in her
math club?
That would be a combination of 18 students taken
4 at a time.
18C4
That would be a permutation of 18 students taken
4 at a time.
Mrs. Spankawitcz has 18 students in her math
class. How many different arrangements are there
for her to pick a president, vice-president,
treasurer, and secretary to be in her math club?
That was easy
18P4
9
Homework
Page 756 - 757 7 22 All Questions Page 766
12 - 38 Even Numbers Only
10
Probability

• Probability is a measure of how likely it is for
  an event to happen.
• We name a probability with a number from 0 to 1.
  
• If an event is certain to happen, then the
  probability of the event is 1.
• If an event is certain not to happen, then the
  probability of the event is 0.

11
Measuring Probability

• If it is uncertain whether or not an event will
  happen, then its probability is some fraction
  between 0 and 1 (or a fraction converted to a
  decimal number).

That sounds pretty easy.
12
Probability Examples
1. What is the probability that the spinner will
stop on part A?
A
B
C
D

• What is the probability that the spinner will
  stop on
• An even number?
• An odd number?

3
1
2
3. What fraction names the probability that the
spinner will stop in the area marked A?
A
C
B
13
Probability Question

• Lawrence is the captain of his track team. The
  team is deciding on a color and all eight members
  wrote their choice down on equal size cards. If
  Lawrence picks one card at random, what is the
  probability that he will pick blue?

blue
blue
green
yellow
black
blue
red
black
14
Probability Question

• Donald is rolling a number cube labeled 1 to 6.
  Which of the following is LEAST LIKELY?
• an even number
• an odd number
• a number greater than 5

15
Compound Probability
And means Multiply
Or means Add
Suppose you roll a blue number cube and a green
number cube. Find the probability of the
following Events.
P(blue 3 or green 5)
P(blue 3 and green 5)
P(blue 1 and green 2)
P(blue 2 or green 6)
That was easy
P(blue 5 or green 8)
P(blue 7 and green 4)
16
Homework
Page 773 10 20 28 32 Even Numbers Only
17
Sample Space
Ive done this before.
Suppose you roll a blue number cube and a green
number cube. List a sample space of all the
possible outcomes.
(1, 1)
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
How many possible combinations are there?
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(3, 6)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
(5, 6)
36 possible combinations
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
List a sample space of all the possible outcomes
if you pick 2 letters, 1 at a time, from the
accompanying letter tiles.
This is just way too easy.
M
A
T
H
(M, A)
(M, T)
(M, H)
(A, M)
(A, T)
(A, H)
How many possible combinations are there?
(T, M)
(T, A)
(T, H)
12 possible combinations
(H, M)
(H, A)
(H, T)
18
Tree Diagram
Suppose Consuela has three children. Draw a tree
diagram showing all the possible combinations and
determine the probability that she has three boys.
Boy
The probability that she has 3 boys is
What is the probability that Consuela has 2 girls
and 1 boy?
Boy
Girl
Boy
Boy
Girl
Girl
Boy
Boy
Girl
Girl
Boy
Girl
Girl
19
Sample Space Tree Diagram

• You have turkey, ham, swiss cheese, american
  cheese, ketchup, and mayonnaise.
• List a sample space of all the possible
  sandwiches you can make using one meat, one
  cheese, and one condiment.
• Draw a tree diagram of all the possible
  sandwiches you can make using one meat, one
  cheese, and one condiment.

K
S
(T, S, K)
(T, S, M)
(T, A, K)
(T, A, M)
M
T
(H, S, K)
(H, S, M)
(H, A, K)
(H, A, M)
K
A
M
Asi De Facil
K
S
M
H
K
A
M
20
Homework
Probability Homework Worksheet Available on
Homework Worksheet Page of Web Site
21
Compound Probabilitywith Replacement
You choose a tile at random from the letter tiles
shown. You replace the first tile and then
choose again. Find the probabilities of the
following.
S
T
E
E
L
E
R
S
F
O
O
T
B
A
L
L
E
E
E
E
E
E
O
O
O
O
E
E
E
O
O
A
E
E
E
O
O
A
S
S
S
S
Remember that and means multiply.
What is the probability that you will choose an E
and then an O?
What is the probability that you will choose a
vowel and then an S?
That was easy
22
Compound Probabilitywithout Replacement
Can I just push the easy button now?
Suppose you have a jar with 6 red marbles, 5 blue
marbles, and 3 green marbles. You take one
marble out and then, without replacing the first
one, you take out a second marble.
Asi De Facil
What is the probability that you will pick a
green one then a blue one?
What is the probability that you will pick two
blue marbles?
That means blue then blue.

23
More Compound Probabilitywithout Replacement
That was easy
Ms. Crabapple has 10 boys and 12 girls in her
class.
If she picks 2 students at random to come up to
the board, what is the probability that she will
pick
a) 2 girls
b) 2 boys
Asi De Facil
24
Homework
Page 780 - 781 8 - 32 Even Numbers Only