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

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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.

I’ve done this before.

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(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)(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.

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

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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;

( )2girlsP1222

1121

132 2462 7

( )2boysP1022

921

90 15462 77

That was easy

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Homework

Page 780 - 781: 8 - 32Even Numbers Only