Quantitative vs Qualitative Quantitative Qualitative Measures quantity and can be described numerically. Age, Weight, Height, Time Describes a category and cannot be measured numerically. Hair Color, Zip Code, Favorite Colo Classify each data set as quantitative or qualitative. Number of students in a class Quantitativ e Phone numbers of students Qualitative Football jersey numbers Qualitative Height of basketball players Quantitativ e That was easy
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Quantitative vs Qualitative QuantitativeQualitative Measures quantity and can be described numerically. Age, Weight, Height, Time Describes a category.
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Quantitative vs Qualitative
Quantitative QualitativeMeasures quantity and can be described numerically.
Age, Weight, Height, Time
Describes a category and cannot be measured numerically.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
Football jersey numbers Qualitative
Height of basketball players Quantitative
That was easy
Types of DataUnivariate Bivariate
Data that uses only one variable.
Data that uses two variables
Weights of football players Lengths and widths of a rectangle
Population:The entire group that you want information about.
Sample: The part of the group that is actually surveyed.
Sampling Methods
Random Systematic StratifiedSurvey a population at random
Survey people whose names are drawn out of a hat
Select a number n at random and survey every nth personSurvey every 5th
person that walks by
Separate a population into smaller groups, then survey each groupSeparate a high school by
grade level, then survey a random sample from each grade
Asi De
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Determining Bias in a Sample
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 biased because the word
exciting makes action films sound more
interesting.
You ask local residents, “Do you prefer action movies or documentaries?”
The question is not biased .
The location where a survey is conducted can also cause a sample to be biased.You ask people leaving Modell’s if they prefer to watch sports or local news on TV. The question is biased
because people shopping at Modell’s 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 .
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.3 27 42 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?
4 3 5 3606 There are 360 possible meals.
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Evaluating Factorials
5!
A factorial is the product of all positive integers less than or equal to a whole number. Does that
say FIVE!!!?
No…it says 5 factorial.
= five factorial
5! 5 4 3 2 1
3!= three factorial
6!= six factorial
120 3! 3 2 16 6! 6 5 4 3 2 1720
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Working with FactorialsHow many different batting order can you have with 9 baseball players?9! 9 8 7 6 5 4 3 2 1
9! 362,880Holy cow! That’s a lot of different possibilities.
A swimming pool has 8 lanes. In how many ways can 8 swimmers be assigned lanes for a race?
8! 8 7 6 5 4 3 2 1 8! 40,320
That was easy
PermutationsThere are 10 runners in a race. In how many different ways can they be assigned a running lane?
10! 10 9 8 7 6 5 4 3 2 1 3,628,800
That’s a factorial.
There are 10 runners in a race. How many arrangements of 1st, 2nd, and 3rd are there?
That’s a permutation.
Method 110 9 8
720
Method 2
10P3
10!10( 3 !)
10!7!
10 9 8 7 6 5 4 3 2 17 6 5 4 3 2 1
720Holy Schnikies! It’s the same answer.
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Combinations &
PermutationsMrs. 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 3,060
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 a president, vice-president, treasurer, and secretary to be in her math club?
That would be a permutation of 18 students taken 4 at a time.
18P4 73,440
(18!
4! 1 )8 4 !
18!1( )8 4 !
That was easy
Homework
Page 756 - 757:7 – 22 All Questions
Page 766: 12 - 38Even Numbers Only
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.
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).
#)
#(
off avorableoutcof possib
omle
eseve
outct
sP n
ome
That sounds pretty easy.
1. What is the probability that the spinner will stop on part A?
2. What is the probability that the spinner will stop on
(a)An even number?(b)An odd number?
3. What fraction names the probability that the spinner will stop in the area marked A?
ABC D
3 12
AC B
Probability Examples
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
yellow
red
green
blue
blue
black
black
• Donald is rolling a number cube labeled 1 to 6. Which of the following is LEAST LIKELY?
A. an even numberB. an odd numberC. a number greater than 5
Probability Question
Compound ProbabilitySuppose you roll a blue number cube and a green number cube. Find the probability of the following Events.
And means Multipl
y
Or means Add
P(blue 3 and green 5)
16
136
P(blue 3 or green 5)
P(blue 1 and green 2)
P(blue 7 and green 4)
P(blue 2 or green 6)
P(blue 5 or green 8)That was easy
16
16
26
16
16
136
16
16
26
16
0 016
16
16
0
Homework
Page 773: 10 – 20 & 28 – 32Even Numbers Only
Sample SpaceSuppose you roll a blue number cube and a green number cube. List a sample space of all the possible outcomes.
List a sample space of all the possible outcomes if you pick 2 letters, 1 at a time, from the accompanying letter tiles.
M A T H
How many possible combinations are there?36 possible combinations
(M, A) (M, T) (M, H)(A, M) (A, T) (A, H)(T, M) (T, A) (T, H)(H, M) (H, A) (H, T)
This is just way too
easy.
How many possible combinations are there?
12 possible combinations
Tree DiagramSuppose Consuela has three children. Draw a tree diagram showing all the possible combinations and determine the probability that she has three boys.
Boy
Girl
Boy
Girl
Boy
Girl
Boy
GirlBoy
Girl
Boy
GirlBoy
Girl
The probability that she has 3 boys is
18
What is the probability that Consuela has 2 girls and 1 boy?
38
Sample Space & Tree Diagram
You have turkey, ham, swiss cheese, american cheese, ketchup, and mayonnaise.a)List a sample space of all the possible sandwiches you can make using one meat, one cheese, and one condiment.b)Draw a tree diagram of all the possible sandwiches you can make using one meat, one cheese, and one condiment.(T, S, K) (T, S, M) (T, A, K) (T, A, M)
(H, S, K) (H, S, M) (H, A, K) (H, A, M)T
H
S
A
S
A
K
MK
MK
MK
M
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Homework
Probability Homework Worksheet
Available on Homework Worksheet Page of Web Site
Compound Probability
with ReplacementYou 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 LE
What is the probability that you will choose an E and then an O?
E E
3(
1)
6P E
E E E O O
2(
1)
6P O
Remember that and means multiply.
O O
( )3 216 16
P E thenO
62
( )56
E thenOP
What is the probability that you will choose a vowel and then an S?
E E E O O A
( )616
vowelP
E E E O O AS S
2(
1)
6P S
6 2(
6 16)
1vowel thenP S
( )12
256vowel thenSP
That was easy
S S
Compound Probability
without Replacement
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.
Can I just push the
easy button now?
What is the probability that you will pick a green one then a blue one?
(4
)31
greenP
5( )
13blueP
( )314
513
theG nP B
( )15182
BP thenG
What is the probability that you will pick two blue marbles?
5( )
14blueP
4( )
13blueP
( )5 414 13
B BP then
20182
( )B BP then
Asi De Facil
That means blue then
blue.
More Compound Probability
without Replacement
Ms. Crabapple has 10 boys and 12 girls in her class.
a) 2 girls
b) 2 boys
If she picks 2 students at random to come up to the board, what is the probability that she will pick;