Population, Parameter, Statistic, Sample A parameter is a numerical summary of the __________________ A statistic is a numerical summary of the ________________ Describing Data What does the 5 – number summary include? What are the 2 summary statistics? Which of the two is influenced by outliers? (circle one) Median Mean You can describe shape as Categorical or Quantitative Variables Categorical Variable: ____________________________________________________________ Quantitative Variable: _____________________________________________________________ Which of the 5 visuals can be utilized for Categorical Variables? ______________________ _______________________ _______________________ Which of the 5 visuals can be utilized for Quantitative Variables? ______________________ _______________________ Visuals What is the difference between a Pareto Chart and a Bar Chart? ___________________________ Match each graph with its Name Pareto Chart Bar Graph Pie chart Box plot Histogram Label each graph with the type of distribution it has ___________ ___________ ____________ ___________ Normal Distribution What is the shape of a normal distribution? ______________________________________________ What does the empirical rule state? ______________________________________________________ *What does a z-score tell you? _________________________________________________________ Population, Parameter, Statistic, Sample You are looking at the average age of all American alligators, you select 15 alligators off the coast of Florida and track them to see how old they become. The average of these 15 live to be 12. The true average age alligators live to is 16. Population: ________________________________________ Parameter: ________________________________________ Sample: __________________________________________ Statistic: __________________________________________ Your dog can jump 2.5 feet. This leads you to believe your dog can jump farther than any other dog. However, the American record book has a dog that can jump 6.48 feet. Population: ________________________________________ Parameter: ________________________________________ Sample: __________________________________________ Statistic: __________________________________________ The Iowa state football team has an average height of 6’2”. The NCAA average height for football players is 6’. You then conclude the ISU team is pretty tall. Population: ________________________________________ Parameter: ________________________________________ Sample: __________________________________________ Statistic: __________________________________________ Oak trees live to be an average age of 263 years. The oak trees in America have been known to live an average of only 123 years. Population: ________________________________________ Parameter: ________________________________________ Sample: __________________________________________ Statistic: __________________________________________ Categorical or Quantitative ____ Top 10 websites ____ Number of roll – over car accidents based on car brand ____ The baggage fees for different airlines collected each year ____ Price of cars people purchased in 2008 ____ Regional rain fall ____ sales for 4 types of smart phones ____ Height of 200 random people in Iowa ____ Net Income ____ Wine exports of the top 5 wine-exporting countries Visuals Draw a Boxplot Draw a Histogram Draw a Bar Chart Normal Using z-scores a) P (Z < 1.5) e) P(Z > z) = 0.60 b) P(Z < z) = 0.35 f) c) P (Z > - 1) g) P (-1 ≤ Z ≤ 1.5) d) P (|Z| < 1.2) h) P(-z < Z < z) = .78 P (Z > 0.5) The times for the 100m freestyle for the womens swim team is evenly distributed with a mean of 59.6 sec. and a standard deviation of 1.2 seconds. a) What time can 50% of the teammates complete a 100m freestyle in? b) What percent of swimmers can complete a 100m freestyle between 58.4 seconds and 60.8 seconds. c) Jane brags that she can swim the race faster than 97.5% of her teammates? What would her time be? d) If Jenny is wanting to make the team and she can swim a 100 m freestyle in 61 seconds, do you think she would make the team? e) What is the probability that one of the girls will beat the opponents fastest swimmer that can swim a 100 m freestyle in 56 seconds? Opening weekend, Marvel films gross sales are normally distributed making an average of $68,326,910 and a standard deviation of $22,442,000. a) X-men only made $55,101,604, how many standard deviations does this movie fall from the mean. b) Thor: The Dark World had an opening box office sales of $85,737,841. What percentile does Thor2 fall under c) The Avengers made $207,438,708. What percentile does this fall under d) If the new spiderman is hoping to hit at least the 40th percentile, how much money is it expecting to make opening weekend in gross sales?