Transcript Document
Chapter 12 and 8-5 Notes 12-1 Frequency Tables, Line Plots, and Histograms Frequency Table: lists each data item with the number of times it occurs. Line Plot: displays data with X marks above a number line. Histogram: shows the frequencies of data items as a graph. 12-1 Frequency Tables, Line Plots, and Histograms Range: _______ 12-1 Frequency Tables, Line Plots, and Histograms-answers 34 5 6 7 5 3 1 1 2 Range: _4______ 12-1 Frequency Tables, Line Plots, and Histograms Range: _______ 12-1 Frequency Tables, Line Plots, and Histograms-answers 0 1 2 3 4 5 2 0 4 1 Range: 4 12-1 Frequency Tables, Line Plots, and Histograms 12-1 Frequency Tables, Line Plots, and Histograms-answers 12-3 Using Graphs to Persuade You can draw graphs of data in different ways in order to give different impressions. You can use a break in the scale on one or both axes of a line graph or a bar graph. This lets you show more detail and emphasize differences. It can also give you a distorted view of the data. 12-3 Using Graphs to Persuade 12-3 Using Graphs to Persuade-answers 1. American Ampersand 2. Fossil Week 3. You might compare lengths of the bars without noticing the break in the scale. 12-3 Using Graphs to Persuade 12-3 Using Graphs to Persuade-answers 12-2 Box-and-Whisker Plots A box-and-whisker plot: displays the distribution of data items along a number line. Quartiles: divide the data into four equal parts. The median is the middle quartile. 12-2 Box-and-Whisker Plots 12-2 Box-and-Whisker Plotsanswers 98 80.5 118 12-2 Box-and-Whisker Plots 12-2 Box-and-Whisker Plotsanswers 13 4 21 8-5 Scatter Plots Scatter Plot: a graph that shows the relationship between two sets of data. Graph data as ordered pairs to make scatter plots. 8-5 Scatter Plots 8-5 Scatter Plots 8-5 Scatter Plots-answers Positive correlation Negative correlation No correlation 12-4 Counting Outcomes and Theoretical Probability To count possible outcomes you can use a tree diagram. 12-4 Counting Outcomes and Theoretical Probability-answers To count possible outcomes you can use a tree diagram. 6 choices AM, AN, BM, BN, CM, CN 8 choices, P1C1, P1C2, P2C1, P2C2, P3C1, P3C2, P4C1, P4C2 12-4 Counting Outcomes and Theoretical Probability To count possible outcomes you can use a tree diagram or count choices using the Counting Principle. Counting Principle: If there are m ways of making one choice, and n ways of making a second choice, then there are m * n ways of making the first choice followed by the second. 12-4 Counting Outcomes and Theoretical Probability Use the Counting Principle to solve each problem. 12-4 Counting Outcomes and Theoretical Probabilityanswers Use the Counting Principle to solve each problem. 5 * 7 * 4 = 140 ways 4 * 13 * 9 = 468 combinations 12-4 Counting Outcomes and Theoretical Probability Theoretical Probability: P(event) = number of favorable outcomes number of possible outcomes 12-4 Counting Outcomes and Theoretical Probability-answers Theoretical Probability: P(event) = number of favorable outcomes number of possible outcomes m1A, m1B, m1C, m2A, m2B, m2C, m3A, m3B, m3C, m4A, m4B, m4C 3/12 simplified to 1/3 1/12 12-5 Independent Events Independent events: events for which the occurrence of one event does not affect the probability of the occurrence of the other. Probability of Independent Events: P(A, then B) = P(A) * P(B) 12-5 Independent Events Probability of Independent Events: P(A, then B) = P(A) * P(B) 12-5 Independent Eventsanswers Probability of Independent Events: P(A, then B) = P(A) * P(B) 1/36 3/36 or 1/12 6/36 or 1/6 2/36 or 1/18 1/36 9/36 or 1/4 Rolling Dice Using the counting principal, how many ways are there to roll 2 die? Make a list of those outcomes. Rolling Dice - answers Using the counting principal, how many ways are there to roll 2 die? 6 x 6 = 36 Make a list of those outcomes. 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, 4-3,4-4,4-5,4-6,5-1,5-2,5-3,5-4,5-5,5-6,61,6-2,6-3,6-4,6-5,6-6 Find the given probabilities if you roll 2 die. P (2 then 3) P (even then 5) P ( 4 then 4) P ( # divisible by 3 then 1) Find the given probabilities if you roll 2 die. - answers P (2 then 3) 1/6 x 1/6 = 1/36 P (even then 5) 3/6 x 1/6 = 3/36= 1/12 P ( 4 then 4)1/6 x 1/6 = 1/36 P ( # divisible by 3 then 1)2/6 x 1/6 = 2/36 = 1/18 Tossing Coins How many ways can 2 coins land? How many ways can 3 coins land? How many ways can 4 coins land? Find the probability if you toss 3 coins: P (heads then heads then heads) P (tails, heads, heads) Tossing Coins - answers How many ways can 2 coins land? 2x2=4 ways How many ways can 3 coins land?2x2x2=8 ways How many ways can 4 coins land?2x2x2x2=16 ways Find the probability if you toss 3 coins: P (heads then heads then heads)1/2x1/2x1/2 = 1/8 P (tails, heads, heads)1/2x1/2x1/2 = 1/8 12-5 Dependent Events Dependent events: events for which the occurrence of one event affects the probability of the occurrence of the other. Probability of Dependent Events: P(A, then B) = P(A) * P(B after A) Dependent Events Dependent Events-answers Probability of Dependent Events: P(A, then B) = P(A) * P(B after A) 1/90 6/90 or 1/15 6/90 or 1/15 4/90 or 2/445 4/90 or 2/45 24/90 or 4/15 Dependent Events Dependent Events-answers Dependent, the total number of cards has been reduced by 1 Independent, the possibilities on the second roll are the same as on the first. Dependent Events Dependent Events Dependent Events-answers 8/100 or 2/25 9/100 12/100 or 3/25 6/100 or 3/50 20/72 or 5/18 20/72 or 5/18 12/72 or 1/6 20/72 or 5/18 12-7 Experimental Probability Experimental Probability: probability based on experimental data. Experimental Probability: P(event) = __number of times an event occurs number of times experiment is done 12-7 Experimental Probability 12-7 Experimental Probability-answers 40%; 6/15 26.7%; 4/15 20%; 3/15 53.3%; 8/15 40%; 6/15 13.3%; 2/15 73.3%; 11/15 0%; 0/15 12-7 Experimental Probability 12-7 Experimental Probability-answers 1/3 2/3 7/33 12-8 Random Samples and Surveys Population: group about which you want information Sample: part of population you use to make estimates about the population. Larger the sample, more reliable your estimates will be. Random Sample: each member of the population has an equal chance to be selected. 12-8 Random Samples and Surveys 12-8 Random Samples and Surveys-answers 320 students 352 students 200 students 192 students 12-8 Random Samples and Surveys 12-8 Random Samples and Surveys-answers Views of people coming out of computer store may not represent the views of other voters. Not a good sample because not random. The city telephone book may cover more than one school district. It would include people who do not vote. Not a good sample, does not represent population. Good sample. People selected at random.