Quantitative vs Qualitative QuantitativeQualitative Measures 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 classQuantitative Phone numbers of studentsQualitative Football jersey numbersQualitative Height of basketball playersQuantitative That was easy

Types of Data UnivariateBivariate 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 RandomSystematic Stratified Survey a population at random Survey people whose names are drawn out of a hat Select a number n at random and survey every nth person Survey every 5 th person that walks by Separate a population into smaller groups, then survey each group Separate a high school by grade level, then survey a random sample from each grade Asi De Facil

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. 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!!!? No…it says 5 factorial. = five factorial = three 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. A swimming pool has 8 lanes. In how many ways can 8 swimmers be assigned lanes for a race? That was easy

Permutations There are 10 runners in a race. In how many different ways can they be assigned a running lane? That’s a factorial. There are 10 runners in a race. How many arrangements of 1 st, 2 nd, and 3 rd are there? That’s a permutation. Method 1Method 2 10 P 3 Holy Schnikies! It’s the same answer. Asi de Facil

Combinations & Permutations 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. 18 C 4 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. 18 P 4 That was easy

Homework Page : 7 – 22 All Questions Page 766: 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.

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? AB CD 31 2 A CB 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 black

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

Compound Probability Suppose you roll a blue number cube and a green number cube. Find the probability of the following Events. And means Multiply Or means Add P(blue 3 and green 5) 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

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

Sample Space Suppose 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. MATH 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 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 Girl Boy Girl Boy Girl Boy Girl Boy Girl Boy Girl Boy Girl The probability that she has 3 boys is What is the probability that Consuela has 2 girls and 1 boy?

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 M K M K M K M Asi De Facil

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. STEELERSFOOTBALLE What is the probability that you will choose an E and then an O?O? EEEEEOO Remember that and means multiply. OO What is the probability that you will choose a vowel and then an S?S? EEEOOAEEEOOASS That was easy SS

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? What is the probability that you will pick two blue marbles? 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; That was easy Asi De Facil

Homework Page : Even Numbers Only