Twins

1. Twins Peter and Paul are twin brothers. One of them (we don’t know which) always lies. The other one always tells the truth. I ask one of them: “Is Paul the one that lies?” “Yes,” he answers. Did I speak to Peter or Paul?

2. Twins I spoke to Peter

3. Average Speed On the way to his grandmother’s house, John travels at an average of 30 mph. On the way back, he travels at an average of 40 mph. What was his average speed for the entire trip?

4. Average Speed Suppose the distance is 120 miles. That means 4hrs there, 3hrs back. That’s 240 miles / 7 hrs = 34.3 mph

5. Review of Last Couple of Weeks Linear or Exponential? Roach population grows 5% every 2 days. Every year, 15 more students attend Matt Forte High School. There has been a $100 increase in wage every 6 months.

6. Review of Last Couple of Weeks Linear or Exponential?

7. Review of Last Couple of Weeks In how many years will a river expanding at 17.35% every year be three times its original size? Use Excel.

8. Making and Interpreting Graphs Week 3

9. What do we use graphs for? • To better communicate information

10. Who uses graphs? • Newspapers • Magazines • Work meetings

11. What types of graphs are there? • Pie chart • XY Graph • Bar Chart

12. When do we use what? • Pie Chart • Limited applicability • Can be used only when you have a quantitative variable associated with a list of categories where both the categories and the quantities each add up to a whole. • The categories must also be disjoint (no overlap) • Common error: to use a pie chart on a set of categories that do not make a whole and to use a pie chart when the categories overlap.  • Use percentage label when using a pie chart

13. Pie Chart Example

14. Pie Chart Example

15. Pie Chart Example

16. Pie Chart Example

17. Pie Chart Example

18. Pie Chart Example

19. Pie Chart Example

20. XY Graphs • AKA line graph (not necessarily a line) • used when you have "a lot" of data points • when categories along the x-axis are numerical • show trends in data clearly • enable the viewer to make predictions about the results of data not yet recorded

21. XY Graph Example

22. XY Graph Example

23. XY Graph Example

24. Bar Graph • use whenever there is a quantitative variable associated with the a categorical variable • For limited amount of data • Succinct • Easy to make comparisons within categories and across categories • Disadvantage: sometimes presents far too much info. • hard to make a single, clear point with them

25. Bar Graph Example

26. Bar Graph Example

27. Bar Graph Example

28. Bar Graph Example

29. Bar Graph Example

30. Bar Graph Example

31. Guidelines for effective graph: • a.  What is the purpose of making a graph from this data? • b.  What type of graph should you make?          pie             bar          x-y scatter (line)    • c.  Decide on a title and consider the the W's (who, what, where and when) • d.  Legend:        yes      no • e.  Descriptive x-axis label (if applicable) • f.  Descriptive y-axis label (if applicable) • g.  Scale (if applicable) • h.   Source

32. Faulty Graphs • People can use graphs to tell you skewed, misleading information.

33. Faulty Graphs

34. Faulty Graphs

35. Faulty Graphs

36. Faulty Graphs

37. Faulty Graphs

38. Faulty Graphs

39. Example 1 • Go to the qrc homepage. Under excel files, find IL_Pop_By_Race.xls and open it. • Add a column which contains the percentage of total population for each racial category. • Make an effective graph.

40. Guidelines for effective graph: • a.  What is the purpose of making a graph from this data? • b.  What type of graph should you make?          pie             bar          x-y scatter (line)    • c.  Decide on a title and consider the the W's (who, what, where and when) • d.  Legend:        yes      no • e.  Descriptive x-axis label (if applicable) • f.  Descriptive y-axis label (if applicable) • g.  Scale (if applicable) • h.   Source

41. Example 2 • Go to the qrc homepage. Under excel files, find DePaulMajors04.xls and open it. • Make an effective graph.

42. Guidelines for effective graph: • a.  What is the purpose of making a graph from this data? • b.  What type of graph should you make?          pie             bar          x-y scatter (line)    • c.  Decide on a title and consider the the W's (who, what, where and when) • d.  Legend:        yes      no • e.  Descriptive x-axis label (if applicable) • f.  Descriptive y-axis label (if applicable) • g.  Scale (if applicable) • h.   Source

43. Make your own faulty graph Change the scale of the y-axis.

44. Make your own faulty graph

45. Make your own faulty graph

46. Make your own faulty graph

48. Example 3 • Go to the qrc homepage. Under excel files, under the folder Chicago, find ChicagoPopulation1830-2000.xls and open it. • Make an effective graph.

49. Guidelines for effective graph: • a.  What is the purpose of making a graph from this data? • b.  What type of graph should you make?          pie             bar          x-y scatter (line)    • c.  Decide on a title and consider the the W's (who, what, where and when) • d.  Legend:        yes      no • e.  Descriptive x-axis label (if applicable) • f.  Descriptive y-axis label (if applicable) • g.  Scale (if applicable) • h.   Source

50. Example 4 • What is wrong with this chart?