Quantitative vs 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 Football jersey numbers Qualitative That was easy Height of basketball players Quantitative

Types of Data Asi De Facil Univariate Bivariate Population: Sample: 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 Random Systematic Stratified 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

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 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. 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

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 No…it says 5 factorial. = six factorial Asi de Facil

Working with Factorials How many different batting order can you have with 9 baseball players? Holy cow! That’s 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?

Permutations That’s 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? That’s a permutation. Method 1 Method 2 10P3 Holy Schnikies! It’s the same answer. Asi de Facil

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

Homework Page 756 - 757: 7 – 22 All Questions Page 766: 12 - 38 Even 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). That sounds pretty easy.

Probability Examples 1. What is the probability that the spinner will stop on part A? B A 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

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

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

Compound Probability That was easy 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)

Homework Page 773: 10 – 20 & 28 – 32 Even Numbers Only

Using a standard deck of cards, answer the following questions Using a standard deck of cards, answer the following questions. Simplify your answers to simplest terms. 1) What is the probability of choosing a red card? b) What is the probability of choosing a seven? 3) What is the probability of choosing a black king or a five? d) What is the probability of choosing an ace of hearts and a club? Asi de Facil

This is just way too easy. Sample Space I’ve 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) (M, T) (M, H) M A T 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)

Tree Diagram Boy Boy Girl Boy Boy Girl Girl Boy Boy Girl Girl Boy Girl Suppose Consuela has three children. Draw a tree diagram showing all the possible combinations and determine the probability that she has three boys. The probability that she has 3 boys is Boy Boy What is the probability that Consuela has 2 girls and 1 boy? Girl Boy Boy Girl Girl Boy Boy Girl Girl Boy Girl Girl

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 c) How many sandwich combinations are there that have american cheese and ketchup? M Asi De Facil K S M H K A M

Homework Probability Homework Worksheet Available on Homework Worksheet Page of Web Site

Compound Probability with 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 S S T E E E E E E E E E E L E E E E E R S S S F O O O O O O O O O O T B A A A L L 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

Compound Probability without 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.

More Compound Probability without 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

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