Intro to Algebra Guided Notes (Unit 11)

Transcription

1 Intro to Algebra Guided Notes (Unit 11) PA 12-1, 12-2, 12-3, 12-7 Alg 12-2, 12-3, 12-4 NAME

2 12-1 Stem-and-Leaf Plots Stem-and-Leaf Plot: numerical data are listed in ascending or descending order. The greatest place value of the data is used for the. The next greatest place value forms the. Key tells you how to the data Given the following test scores, make a stem-and-leaf plot Make a Stem-and-Leaf Plot for each set of data

3 12-2 Measures of Variation Measures of Variation: the following measurements which are used to the of. Mean: Median: Mode: Range: between the greatest and least values (G-L) Quartiles: that divide the data into equal parts (LQ, M, UQ) Interquartile Range (IQR): between the upper and lower quartiles (UQ-LQ) Outliers: data values that are the value of the IQR outside the quartiles Find the range, interquartile range, and any outliers for {36, 30, 61, 21, 34, 27}. Using measures of variation to interpret and compare data: The maximum allowable speed limits for certain western and eastern states are listed in the stem-and-leaf plot. a. What is the median speed limit for each region? b. Compare the western states range with the eastern states range.

4 1. Find the range, interquartile range, and any outliers for: a. {49, 6, 40, 62, 51, 35, 43}. b. {42, 49, 53, 41, 44, 67, 61, 55}. 2. The average monthly temperatures of Tucson, Arizona, and Hot Springs, New Mexico, are listed in the stem-and-leaf plot. a. What is the median temperature for each city? b. Compare Tucson s range with Hot Springs range.

5 12-3 Box-and-Whisker Plots Box-and-Whisker Plots: divides a set of data into parts using the median and 2 quartiles. A is drawn around the quartile values, and extend from each quartile to the and values. Inter-quartile Range is the between the and quartiles. Box-and-whisker plots separate data into four parts. The parts may differ in length. Each part is 25% of the data. Make a box-and-whisker plot for the following data: Make a Box-and-Whisker Plot for each set of data

6 12-7 Simple Probability Probability is the likelihood something will occur. P (event) = Number of favorable outcomes Total number of outcomes An event that is certain to occur has a probability of 1 or 100%. An event that is impossible has a probability of 0. Example: A bag contains 7 pink, 2 white, and 6 blue marbles. One marble is selected without looking. Find P(blue). Then describe the likelihood of the event. Example: Katy rolls a six-sided number cube whose sides are numbered 1 through 6. Find P(even). Then describe the likelihood of the event. The spinner shown at left is spun once. Determine the probability of each outcome. Express each probability as a fraction and as a percent. a.) P(6) d.) P(even) b.) P(greater than 6) e.) P(less than 5) c.) P (not even) f.) P(not 11)

7 12-7 Simple Probability (Day 2) Theoretical Probability of an event is what should occur when conducting an experiment Examples: Flip a coin P(heads) Standard deck of cards P(picking a club) P(picking a black card) P(picking a King) Experimental probability of an event is what actually occurs during an experiment Ex. 1: The table shows the results of an experiment in which a number cube was rolled. Find the experimental probability of rolling a six for this experiment. Then compare it with the theoretical probability. Experimental Probability Theoretical Probability Ex. 2: Find the experimental probability of rolling a four for the experiment above. Then compare it to the theoretical probability.

8 Algebra 12-2 Counting Outcomes Tree diagram one method used for the number of possible outcomes. Sample space - the list of all outcomes. Event a collection of one or more in the sample space. EX: At football games, a concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham and then you choose either chips, a brownie or fruit. Make a tree diagram to show the number of possible combinations. The Fundamental Counting Principle says that you can take each event and multiply the choices. (Above example would be = 18) EX: When ordering a certain car, there are 7 colors for the exterior, 8 colors for the interior, and 4 choices of interior fabric. How many different possibilities are there for color and fabric when ordering this car? Factorial is the of all positive integers beginning the first number and counting backward to 1. ( It is written as n!, where n is greater than 0) EX: 8! = = 40,320

9 EX: There are 8 students in the Algebra Club. The students want to stand in a line for their yearbook picture. In how many different ways can the 8 students stand for the picture? EX: Find the value of 12! EX: A couple is going to a national park for their vacation. Near the campground where they are staying, there are 6 hiking trails. a. How many different ways can they hike all the trails if they hike each trail only once? b. If they only have time to hike 4 of the trails, in how many ways can they do this?

10 Algebra 12-3 Permutations and Combinations Permutation An arrangement or listing in which or placement is important. The number of permutations of n objects taken r at a time is the quotient of n! and (n-r)! n! P = n r ( n r)! EX: The manager of a coffee shop needs to hire two employees, one to work at the counter and one to work at the drive-through window. Katie, Bob and Alicia all applied for a job. How many possible ways can the manager place them? Think: How many objects? Taken how many at a time? EX: A combination bike lock requires a three-digit code made up of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. No number can be used more than once. How many different permutations can be made? EX: A club with 10 members wants to choose a president, vice-president, secretary, and treasurer. How many different sets of officers are possible? EX: Evaluate P 12 3

11 Combination an arrangement or listing in which order is important. The number of combinations of n objects taken r at a time is the quotient of n! and (n-r)!r! n! C = n r ( n r)! r! EX: A group of 7 seniors, 5 juniors, and 4 sophomores have volunteered to be peer tutors. Mrs. Geissler needs to choose 12 students out of the group. How many ways can the 12 students be chosen? Hint: Order does NOT matter, so there are 16 students taken 12 at a time. EX: A diner offers a choice of two side items from a list of 8 items. How many ways can two items be selected? EX: The coach had to select 5 out of 12 players on his basketball team to start the game. How many different groups of players could be selected to start the game? EX: Evaluate C 7 3 EX: Who is correct in evaluating C? 6 4 Eric 6 6! = 360 OR Melissa 2!4!! 2! = 15

12 Algebra 12-4 Probability of Compound Events Compound Event consists of two or more simple events Probability of Compound events is the probability that a compound event will occur. Example: Dan is going to spin each spinner once. What is the probability that he will spin red and the number 9? ~Step 1 find the probability of each event ~Step 2 Multiply both to find the probability of spinning a red and 9. Ex: You have a bag filled with balls. There is one red, one blue, one yellow, one green, one purple, and one pink. Without looking, you pull out one ball, without putting it back, you pull out another ball. What is the probability of you pulling a red ball the first time and a yellow ball on the second time? What is the probability of you NOT pulling a red ball the first time and a yellow ball on the second time?