1.  Display Quantitative Variables appropriately  Describe a distribution correctly  Compare 2 distributions correctly  Know how to graph a trend over time AP Statistics Objectives Ch4

2.  Distribution  Histogram  Relative Frequency Histogram  Stem-and-leaf Display  Dotplot  Shape Vocabulary  Center  Spread

3.  Mode  Unimodal  Bimodal  Uniform  Symmetric  Tail Vocabulary  Skewed  Outliers  Gaps  Timeplot  Re-expressing Data  Skewed right? Try Sqrt or Log  Skewed left? Try Squaring

4. Timeplot Vocabulary Calculator Skills Chapter 3 Assignment Answers Chapter 4 Assignment

5. Chapter 4 Assignment Pages 65 – 67 Problems #5, 12, 14, 19, 20

6. DWF High Temperatures July 2012 Day in July of 2011 5 15 10 20 25 30 High Temp (F o ) 95 100 105

7. Chapter 4 Vocabulary gives the possible values of a variable and the frequency and/or relative frequency of each value 1. Distribution-

8. Chapter 4 Vocabulary uses adjacent bars to show the distribution of values in a quantitative variable, where each bar represents the frequency of values falling in an interval of values. 2. Histogram-

9. 3. Relative Frequency Histogram- Chapter 4 Vocabulary uses adjacent bars to show the distribution of values in a quantitative variable, where each bar represents the relative frequency of values falling in an interval of values.

10. Chapter 4 Vocabulary shows quantitative data values in a way that sketches the distribution of the data 4. Stem-and-leaf Display-

11. Chapter 4 Vocabulary 5. Dotplot- graphs a dot for each case against a single axis

12. Chapter 4 Vocabulary 7. Center- always used to describe a histogram by noting the number of modes (humps) and the symmetry or skewness observed 6. Shape- always used to describe a histogram by providing a single “typical” value (Coming…. Measures of Central Tendency) 8. Spread- always used to describe a histogram by providing a numerical summary of how tightly the values are clustered around the “center”

13. Chapter 4 Vocabulary 10. Unimodal- a hump or local high point in the shape of the distribution of a variable Note: that their location and number can change as a histogram’s bin size changes 9. Mode- having one mode (aka mound-shaped) 11. Bimodal- having two modes

14. Chapter 4 Vocabulary 13. Symmetric- describes a distribution that is roughly flat 12. Uniform- describes a distribution for which the two halves on either side of the center look approximately like mirror images of each other

15. Chapter 4 Vocabulary 15. Skewed- the parts of a distribution that typically trail off on either side 14. Tail- Describes a distribution that is not symmetric and for which one tail stretches out farther than the other SKEWED RIGHT – right tail longer SKEWED LEFT – left tail longer

16. Chapter 4 Vocabulary extreme values that don’t appear to belong with the rest of the data -indicates more investigation is needed -ALWAYS COMMENT ON THEM WHEN THEY ARE FOUND 16. Outliers-

17. Chapter 4 Vocabulary 17. Gaps- Spaces in between the bars of a histogram -ALWAYS COMMENT ON THEM WHEN THEY ARE FOUND

18. Chapter 4 Vocabulary displays data that change over time Often, successive values are connected with lines to show trends more clearly. 18. Timeplot-

19. Chapter 4 Vocabulary 19. Re-expressing Data- a.k.a. Transforming data Using a function on data to produce a graph which is easier to use -variables that have a distribution that is skewed to the right often benefit from a re-expression by logarithms or square roots -skewed to the left may benefit from squaring the data values

20. Calculator Skills: Display Histogram 1)Enter data in STAT EDIT 2) Go to 2 nd Y= (STATPLOT) a)Choose 1:Plot1 3) In the Plot1 screen: a)Choose On b)Choose Histogram Icon c)Place List Name in Xlist: d)If all values in one list, then Freq: is 1 Else Freq: is a List Name

21. 4) Go to ZOOM 9 (ZoomStat) Calculator Skills: Display Histogram 3) In the Plot1 screen: a)Choose On b)Choose Histogram Icon c)Place List Name in Xlist: d)If all values in one list, then Freq: is 1 Else Freq: is a List Name TI-83 & TI-84 do a poor job with bin size. Change it.

22. Calculator Skills: Sort Ascending Order 1) STAT 2 (SortA) 2)Tell calculator which list to sort: a) L1 is 2 nd 1 b) L2 is 2 nd 2 :::: f) L6 is 2 nd 6 g)OR just 2 nd STAT (LIST) and choose the one you want

23. Cause of DeathPercent Heart disease30.3 Cancer23.0 Circulatory diseases and stroke8.4 Respiratory diseases7.9 Accidents4.1 7. The Center for Disease Control lists causes of death in the United States during 1999. a) Is it reasonable to conclude that heart or respiratory diseases were the cause of approximately 38% of U.S. deaths in 1999? Explain. 30.3 + 7.9 = 38.2 “yes” w/o reasoning would be a Partial

24. Cause of DeathPercent Heart disease30.3 Cancer23.0 Circulatory diseases and stroke8.4 Respiratory diseases7.9 Accidents4.1 7. The Center for Disease Control lists causes of death in the United States during 1999. b) What percent of deaths were from causes not listed here? (Show work) 100 – 73.7 = 26.3

25. Cause of DeathPercent Heart disease30.3 Cancer23.0 Circulatory diseases and stroke8.4 Respiratory diseases7.9 Accidents4.1 7. The Center for Disease Control lists causes of death in the United States during 1999. c) Create an appropriate display for these data. 20% 40% 60% 80% 100% 0% Other 26.3% Causes of Death

26. Chapter 3 # 10 A study by the US Bureau of Alcohol, Tobacco, and Firearms (BATF) (USA Today, 22 June 2000) surveyed 1530 investigations by the US BATF into illegal gun trafficking from July 1996 through December 1998. The study reports the portion of cases that were the result of each of five gun trafficking violations: 46% Straw purchase (legal gun buyer acting on behalf of an illegal buyer) 21% Unlicensed sellers 14% Gun shows and flea markets 14% Stolen from federally licensed dealers 10% Stolen from residence

27. Chapter 3 # 10 a) State the W’s for this study to the extent the story gives them. Who: Data was collected about illegal gun trafficking investigations. What: Number of gun trafficking violations by type of violation Where: The data were collected in the U.S. When: The study included data from July 1996 through December 1998. How: The data were collecting by surveying 1530 investigations.

28. Chapter 3 # 10 A study by the US Bureau of Alcohol, Tobacco, and Firearms (BATF) (USA Today, 22 June 2000) surveyed 1530 investigations by the US BATF into illegal gun trafficking from July 1996 through December 1998. The study reports the portion of cases that were the result of each of five gun trafficking violations: 46% Straw purchase 21% Unlicensed sellers 14% Gun shows and flea markets 14% Stolen from federally licensed dealers 10% Stolen from residence b) What do you notice about the percentages listed? What does that probably mean? The percentages total to more than 100%. Either a case may be assigned to more than one category or one or more of these numbers are wrong.

29. Chapter 3 # 10 46% Straw purchase 21% Unlicensed sellers 14% Gun shows and flea markets 14% Stolen from federally licensed dealers 10% Stolen from residence c) Make a bar chart to display these results, and label it correctly.

30. 10. A study by the US Bureau of Alcohol, Tobacco, and Firearms (BATF) (USA Today, 22 June 2000) surveyed 1530 investigations by the US BATF into illegal gun trafficking from July 1996 through December 1998. The study reports the portion of cases that were the result of each of five gun trafficking violations: 46% Straw purchase 21% Unlicensed sellers 14% Gun shows and flea markets 14% Stolen from federally licensed dealers 10% Stolen from residence d) Write a brief summary on what they say about illegal gun trafficking. Note any possible problems with the data. Nearly half of the illegal gun trafficking cases were due to straw purchases. More than 1 in 5 of the illegal gun trafficking cases were due to unlicensed sellers. The percentages total to over 100%, which could indicate an error in the data.

31. e) The study also noted that although corrupt licensed dealers accounted for 133 of the 1530 investigations, they were linked to 40,365 of the 84,128 firearms involved in those investigations. How does this new information about the Who of the study affect your conclusions? The percentages would be quite different if we had based them on the number of firearms instead of investigations. Some investigations had many firearms associated with them. Note: 133 cases involving corrupt licensed dealers is only about 9% of the 1530 investigations, but these cases accounted for almost 50% of the firearms involved in all of these investigations…..

32. Chapter 3 # 18 Students in an Intro Stats course were asked to describe their politics as “Liberal”, “Moderate”, or “Conservative.” Here are the results: a)Complete the table above by correctly first filling in the two missing cells and then the margin totals for Politics. (see above) b)What percent of the class is male? (show work) 115/192 = 0.5989583333 About 60% of all students questioned are male.

33. Chapter 3 # 18 Students in an Intro Stats course were asked to describe their politics as “Liberal”, “Moderate”, or “Conservative.” Here are the results: c) What percent of the class considers themselves to be “Conservative”? 27/192 = 0.140625 About 14% of all students questioned are “Conservative.”

34. Chapter 3 # 18 Students in an Intro Stats course were asked to describe their politics as “Liberal”, “Moderate”, or “Conservative.” Here are the results: d) What percent of the males in the class consider themselves to be “Conservative”? 21/115 = 0.1826086957 About 18% of all males questioned are “Conservative.”

35. Chapter 3 # 18 Students in an Intro Stats course were asked to describe their politics as “Liberal”, “Moderate”, or “Conservative.” Here are the results: e) What percent of all students in the class are males who consider themselves to be “Conservative”? 21/192 = 0.109375 About 11% of all students questioned are males who consider themselves to be “Conservative.”

36. Chapter 3 # 18 Students in an Intro Stats course were asked to describe their politics as “Liberal”, “Moderate”, or “Conservative.” Here are the results: f) What percent of all females in the class are “Liberals”? 35/77 = 0.45454545 About 45% of all females questioned are “Liberals.”

37. Chapter 3 # 18 Students in an Intro Stats course were asked to describe their politics as “Liberal”, “Moderate”, or “Conservative.” Here are the results: g) What percent of all males in the class are “Liberals”? 50/115 = 0.4347826 About 43% of all males questioned are “Liberals.”

38. Chapter 3 # 18 Students in an Intro Stats course were asked to describe their politics as “Liberal”, “Moderate”, or “Conservative.” Here are the results: h) Do politics and sex appear to be independent? The conditional distributions of gender differ. 18.3% of males are conservative, while for females only 7.8% are conservative. There appears to be an association between politics and sex. Female: 45% Liberal, 47% Moderate, 8% Conservative Male: 43% Liberal, 38% Moderate, 18% Conservative

39. 31. A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level. A G E Under 3030-49Over 50 Low 273731 Normal 489193 High 235173 BLOOD PRESSURE a) Fill in the missing marginal totals above.

40. 31. A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level. A G E Under 3030-49Over 50 Low 273731 95 Normal 489193 232 High 235173 147 98179 197 474 BLOOD PRESSURE

41. 31. A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level. A G E Under 3030-49Over 50 Low 273731 95 Normal 489193 232 High 235173 147 98179 197 474 BLOOD PRESSURE c) Find the Conditional Distribution of blood pressure level within each age group. Under 30: 28% low, 49% normal, 23% high 30-49: 21% low, 51% normal, 28% high Over 50: 16% low, 47% normal, 37% high

42. 31. A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level. A G E BLOOD PRESSURE d) Compare these distributions with a segmented bar graph. Under 30: 28% low, 49% normal, 23% high 30-49: 21% low, 51% normal, 28% high Over 50: 16% low, 47% normal, 37% high

43. 31. A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level. A G E BLOOD PRESSURE e) Write a brief description of the association between age and blood pressure among these employees. The distributions are different for each of the age categories, so there appears to be an association between age and blood pressure. In this company, as age increases, the percentage of employees with low blood pressure decreases, and the percentage of employees with high blood pressure increases. Under 30: 28% low, 49% normal, 23% high 30-49: 21% low, 51% normal, 28% high Over 50: 16% low, 47% normal, 37% high

44. 31. A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level. f) Does this prove that people’s blood pressure increases as they age? Explain. No, this does not prove that people’s blood pressure increases as they age. An association between two variables does not imply a cause-and-effect relationship. Only a controlled experiment can isolate the relationship between age and blood pressure.