Statistics and the Common Core
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- Scatterplot Interpretation
- Dice and the Transitive Property
Comparing DistributionsUsing relevant measures of center, spread NAME____________________________ Compare the distributions in context using appropriate measures of center and spread. Average age at death of the ten most common last names among the deceased persons in Olathe, KS and Milton, IN. From city-data.com 1. Counts of the lengths of all words in Obama and G. W. Bush’s second inaugural addresses 2. Annual number of tropical storms and hurricanes in the Western Pacific (1851 to 2013) . 3. This data set comes directly from the "Is Wal-Mart Safe?" report. The study focused on 32 Wal-Mart that experienced the “highest rate” of reported police incidents in 2004. Target stores chosen for the comparative analysis were within a 10-mile radius of the 50 “high incident” Wal-Mart stores. Average speeds of winning drivers of all Daytona 500 (1959-2014) and Indy 500 (1911 to 2014) races. 4. 5. This is the same data as the previous problem, but now the comparison is for the years when both races occurred, 1959-2014. How is the comparison different this time? 6. Willerman et al. (1991) collected a sample of 40 right-handed Anglo introductory psychology students at a large southwestern university. The researchers used Magnetic Resonance Imaging (MRI) to determine the brain size of the subjects. 7. Total home runs hit per team in Major League Baseball in 2013. 8.
Scatterplot InterpretationDescribing associations NAME____________________________ 1. Describe what the following graph tells you about the first 8 days of Old Faithful eruptions in January, 2011. 2. Here is a graph showing the time between eruptions for the first 999 eruptions of 2011. Do you think this is why “Old Faithful” got its name? Explain. (And what could have caused the outlier?)
5. Kentucky Derby winning horse times: describe the association vs. year. Also explain why the shape of the distribution is what you see depicted here (including the outlier). 6. Kentucky Derby winning horses’ average time: describe the association vs. year. Also give an explanation as to the large gap in times. 7. Describe the association between life expectancy and the number of TV’s per person for the following 22 countries. Also fully explain what the graph does NOT show. 8. Describe what the following graphs show about tropical storms and hurricanes in the North Atlantic and the Western Pacific. North Atlantic Tropical Storms and Hurricanes Western Pacific Tropical Storms and Hurricanes Dice and the Transitive PropertyProbability modeling with dice NAME____________________________ A standard six-sided die contains the numbers 1,2,3,4,5,6. This activity uses special non-standard dice that have the following numbering schemes: Green die: 4,4,4,4,4,1 Blue die: 3,3,3,3,3,6 Black die: 2,2,2,5,5,5 1. What is the mean roll of a standard die? _______ Interpret this mean. 2. What is the mean roll of the non-standard dice? Green:_______ Blue:_______ Black:______ 3. How to the means compare (standard die vs. non-standard dice)? What does this mean? 4. Let’s say you are going to play a game in which you and a friend each choose a different non-standard die to roll, and the highest roll wins. Do you think this would be a fair game in the long run? Simulate many rolls using any two dice of your choice. Using tally marks, count the number of times each die wins. Green vs. Blue: Green: Blue: Blue vs. Black: Blue: Black: Black vs. Green: Black: Green:
Green’s winning percentage vs. Blue = _______________ Blue’s winning percentage vs. Black = ________________ Black’s winning percentage vs. Green = ________________ So the ___________ die has an advantage over the _____________ die. The ___________ die has an advantage over the _____________ die. And the ___________ die has an advantage over the _____________ die. How can this be true when they all have the same mean roll??? The answer lies in the fact that we are interested in the _______________________ of the rolls each time, not the long run average over a long period of time. 6. To prove this mathematically, we need to make a table of the differences between two dice. Let’s start with Green vs. Blue. List all the differences (Green minus Blue) in the table below.
How many different rolls are possible? ____________ Summarize the table above in the table below (Prob = “probability”):
In what fraction of the rolls does Green beat Blue? ___________ Since this fraction is greater than 50%, we can say that the Green die has the advantage over the Blue die in the long run. Both tables are examples of probability models, and they can help us prove mathematically how random events will behave (in the long run). If you created probability models for Blue vs. Black and Black vs. Green, you can prove that these dice are non-transitive! Do you know of any other relationships like this that are non-transitive? From the AP Statistics Exam: 1999 #5 Die A has four 9’s and two 0’s on its faces. Die B has four 3’s and two 11’s on its faces. When either of these dice is rolled, each face has equal chance of landing on top. Two players are going to play a game. The first player selects a die and rolls it. The second player rolls the remaining die. The winner is the player is the player whose die has the higher number on top. A. Suppose you are the first player and you want to win the game. Which die would you select? Justify your answer. B. Suppose the player using die A receives 45 tokens each time he or she wins the game. How many tokens must the player using die B receive each time he or she wins in order for this to be a fair game? (A fair game is one in which the player using die A and the player using die B both end up with the same number of tokens in the long run) Explain how you found your answer. Download 283.31 Kb. Share with your friends:
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