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Name ______________________________ Block _____ STATISTICS Unit 2 STUDY GUIDE – Topics 6-10 Part 1: Vocabulary For each word, be sure you know the definition, the formula, or what the graph looks like. A. association M. mean absolute deviation Y. side-by-side stemplot B. boxplot N. median Z. Simpson‟s paradox C. center O. mode AA. standard deviation D. conditional distribution P. modified boxplot BB. standardization E. empirical rule Q. outliers CC. stemplot F. five-number summary R. outlier test DD. symmetric G. histogram S. range EE. two-way table H. independent T. relative risk FF. upper quartile I. interquartile range U. resistant GG. variability J. lower quartile V. segmented bar graph HH. z-score K. marginal distribution W. skewed left L. mean X. skewed right _______ 1. A graph for a quantitative variable that divides a distribution into 25% segments. _______ 2. A graph for a quantitative variable that divides a distribution into 25% segments and shows all mathematical outliers. _______ 3. The minimum, Q1, median, Q3, and maximum. _______ 4. The “middle” of a distribution that can be described by the mean, median, or mode. _______ 5. The “middle” of a distribution that is also known as the average. _______ 6. The “middle” of a distribution that is the most frequently occurring number. _______ 7. The “middle” of a distribution that divides the list of numbers in half. _______ 8. A graph for a quantitative variable that has a column for part of the numbers and rows for the other part of the numbers. _______ 9. A graph for a quantitative variable and a categorical binary variable that has a column for part of the numbers and rows off to the left and right for the other part of the numbers. _______ 10. The description of a distribution‟s shape that has a peak in the middle and tapers off evenly to the left and to the right. _______ 11. The description of a distribution‟s shape that has a peak on the left and tapers off to the right. _______ 12. The description of a distribution‟s shape that has a peak on the right and tapers off to the left. _______ 13. 68% of the data falls between – 1 and + 1 standard deviations, 95% of the data falls between – 2 and + 2 standard deviations, and 99.7% of the data falls between – 3 and +3 standard deviations _______ 14. Q3 – Q1 _______ 15. maximum – minimum _______ 16. Q3 + (IQR * 1.5) and Q1 – (IQR * 1.5) _______ 17. The proportion of an event in one category compared to the proportion of the same event in a different category. This value tells you how many times more likely the event is to occur in the first category than in the second. _______ 18. Q3 This value divides a distribution into 75% and 25% segments. _______ 19. Q1 This value divides a distribution into 25% and 75% segments. _______ 20. A value (or values) that are significantly far away from the rest of the data. _______ 21. A measure of spread that is calculated by (1) subtracting the mean from each number in a distribution, (2) taking the absolute value of each of the differences, then (3) taking the average of these differences. _______ 22. A measure of spread that is calculated by (1) subtracting the mean from each number in a distribution, (2) squaring the differences, (3) adding the squared values, (4) dividing that sum by n – 1, and (5) taking the square root of the quotient. _______ 23. When one variable has an affect on another variable, there is this between them. _______ 24. When one variable does not have any affect on another variable, they are said to be this. _______ 25. A graph for two categorical variables where one of the variables is represented in columns and the other variable is represented as segments within the columns. _______ 26. This is a measure of standard deviations. _______ 27. A phenomenon where overall proportions contradict proportions in separate categories. _______ 28. The process of measuring different distributions in standard deviations so comparisons can be made between them. _______ 29. A tool for organizing two categorical variables in rows and columns. _______ 30. Proportions that are calculated within the columns of a two-way table. _______ 31. Proportions that are calculated within the margins of a two-way table. _______ 32. A measurement that doesn‟t change when outliers are present is said to be this. _______ 33. Another term for the spread. _______ 34. A graph for a quantitative variable that is similar to a dotplot, but uses columns. Part 2: General Knowledge Questions 35. What are the different measures of center? _________________________ _________________________ _________________________ 36. What are the different measures of spread? _________________________ _________________________ _________________________ 37. What are the 3 different shapes a distribution can have? _________________________ _________________________ _________________________ 38. What are the five values listed in the five-number summary? _______________ _______________ _______________ _______________ _______________ 39. Based on the five-number summary, what percent of the data falls: Below the Q1? _______________ Between the Q1 and the Q3? _______________ Below the Median? _______________ Between the Min and the Q3? _______________ Below the Q3? _______________ Between the Q1 and the Max? _______________ 40. For a normal distribution, what is the proportion of data that falls within: one standard deviation of the mean? _______________ two standard deviations of the mean? _______________ three standard deviations of the mean? _______________ What is this pattern called? ________________________________________ Using the histograms provided, choose the most appropriate graph for each description. _____ 41. The mean is greater than the median. _____ 44. The median is greater than the mean. _____ 42. The standard deviation is largest. _____ 45. The graph is a normal distribution. _____ 43. The graph is skewed left. _____ 46. The graph is skewed right. A. B. C. D. Match each of the following graphs with the proper description. _____ 47. Bar Graph _____ 51. Modified Box Plot _____ 48. Box Plot _____ 52. Segmented Bar Graph _____ 49. Dot Plot _____ 53. Stem Plot _____ 50. Histogram A. B. C. D. F. E. KEY: G. 0 5 5 6 8 1 0 1 3 4 7 9 9 9 2 0 0 1 2 3 5 For each of the graphs, state what type of variables are represented by that type of graph and how many variables can be represented at a time. graph 54. Bar Graph 55. Box Plot 56. Dot Plot 57. Histogram 58. Modified Box Plot 59. Scatter Plot 60. Segmented Bar Graph 61. Stem Plot number of variables type of variables Match each term with the appropriate letter, formula, or equation. Please use capital letters. A. Max – Min B. z= x-μ σ C. Q1 – (1.5*IQR) _____ 62. The interquartile range. _____ 63. Test for lower outliers. _____ 65. Test for upper outliers. _____ 66. The z-score. D. Q3 + (1.5*IQR) E. Q3 – Q1 _____ 64. The range. Part 3: Short Answer / Extended Response Topic 6: Given the number of times an event occurs out of how many total occurrences for two different groups, you should be able to create a two-way table, a segmented bar graph and calculate the relative risk. Toward the end of 2003, there were many warnings that the flu season would be especially severe and many more people chose to obtain a flu vaccine than in previous years. In January 2004, the Centers for Disease Control and Prevention magazine published the results of a study that looked at workers at Children‟s Hospital in Denver, Colorado. Of the 1000 people who had chosen to receive the flu vaccine (before November 1, 2003), 149 still developed flu-like symptoms. Of the 402 people who did not get the vaccine, 68 developed flu-like symptoms. a. Create a two-way table for the data in the paragraph above. TOTAL TOTAL b. Calculate the conditional distributions and write the proportions in the lower right corners of the table. c. Create a segmented bar graph based on the conditional distributions. KEY: d. What is the relative risk of developing flu-like symptoms? Show all work. e. Are these variables independent? __________ Why or why not? Topic 7: Given quantitative data or quantitative data that is divided into categories, you should be able to create a histogram, a stemplot, or a side-by-side stemplot then describe the distribution using SOCS. Arby’s Sandwiches Arby‟s Melt with Cheddar Arby Q Bac‟n Cheddar Deluxe Beef „n Cheddar Giant Roast Beef Junior Roast Beef Regular Roast Beef Super Roast Beef Breaded Chicken Fillet Chicken Cordon Bleu Grilled Chicken BBQ Grilled Chicken Deluxe Roast Chicken Club Roast Chicken Deluxe a. Create a histogram of the Arby‟s data. b. Describe the distribution using SOCS. fat/oz 3.5 * 2.8 4.2 * 4.2 * 3.5 3.2 3.5 3.1 3.9 3.9 * 1.8 2.5 * 3.6 * 2.9 * Arby’s Sandwiches Roast Chicken Santa Fe French Dip Hot Ham „n Swiss Italian Sub Philly Beef „n Swiss Roast Beef Sub Triple Cheese Melt Turkey Sub Roast Beef Deluxe Roast Chicken Deluxe Roast Turkey Deluxe Fish Fillet Ham „n Cheese Ham „n Cheese Melt fat/oz 3.4 3.2 2.5 * 3.6 * 4.5 * 3.9 5.4 * 2.8 1.6 0.9 1.0 3.5 2.4 * 2.7 * c. Create a stemplot for the Arby‟s data. Rough Draft: Final Copy: d. Create a side-by-side stemplot for the Arby‟s data (An asterix indicates a sandwich with cheese, those without an asterix do not have cheese.) e. Describe the cheese distribution and the no cheese distribution using SOCS. Topic 8: Given quantitative data in a list or in a table, you should be able to calculate the mean, the median and the mode. Also, look over the review packet from this topic. The main concepts were mean, median, mode, comparing dotplots, and using a calculator to generate the 3 measures of center. a. The table represents the number of friends students reported having in their first block class. Determine each of the three measures of center from the table. (Round to the nearest tenth if rounding is necessary.) # friends 1 2 3 4 5 6 7 8 frequency 0 1 2 7 15 18 12 10 mean = __________ median = __________ mode = __________ b. Use the Arby‟s data from the Topic 7 example to calculate each of the following measurements. Check your answers by entering the data into your calculator. Using 1-Var Stats and a calculator-generated dotplot. (Round to the nearest tenth.) mean = __________ median = __________ shape = ____________________ mode = __________ spread = ____________________ Topic 9: Look over your review sheets from this chapter. The main concepts were range, IQR, and standard deviation. We also calculated the MAD and standard deviation by hand, looked at the Empirical Rule and z-scores so we could compare distributions that were measured on different scales. Topic10: Look over your review sheets from this chapter. The main concepts were boxplots, modified boxplots, the 5-number summary and calculating outliers. We also used our calculator to send groups, ungroup them, modify lists, sort lists (with an ID list), and create graphs. Use the Five-Number Summary to answer #8 - 11. Minimum Q1 Median Q3 Maximum 7 15 18 33 75 a. What is the IQR? _______________ b. What is the range? _______________ b. An upper outlier would be any number that falls above what value? c. A lower outlier would be any number that falls below what value? d. Construct a regular boxplot for the data above. e. Would it be possible to make a modified boxplot? __________ Why or why not?