1. STATS 250 Lab 2 Julie Ghekas jghekas@umich.edu September 15, 2014

2. Schedule Recap from first lab and prelab Warm Up Lab 2 Cool Down iClicker Questions

3. Lab Workbook for Fall 2014 open.umich.edu/ – Search Stats 250 – Select Materials Tab for the course – Scroll down to have access to handouts, labs, lecture notes, etc. open.umich.edu/education/lsa/statistics250/fall2015/mater ials#Labs Or order from Amazon (~$10) Recommend taking notes in updated personal workbook

4. Prelab Results Right skewed: Mean > Median Left skewed: Median > Mean Symmetric: Mean = Median Remember, the mean is more sensitive to outliers than the median.

5. Recap for Homework Practice homework graded to the same standard of regular homework Answer the question fully Put your name on generated graphs Show all work Include units

6. Boxplots Graph of 5-number summary Outliers denoted w ith ° and * Can be side-by-side Does not show shape of distribution

7. Bar charts Displays categorical variables Y-axis represents counts, proportions, or percentages Can rearrange bars in any order

10. Time Series/Sequence Plots Examining data over time Checks assumption that observations are from an identically distributed population Be careful; time series can be displayed in different formats

11. Time Series Source: http://www.statcan.gc.ca/edu/power- pouvoir/ch9/bargraph- diagrammeabarres/5214818-eng.htm Source: http://blogs.bgsu.edu/statgraphicsmep aler/2013/03/22/new-havens- temperature-in-4-different-time- series-plots/

12. Time Series: Trends A trend is a consistent, long-term rise or fall.

13. Time Series: Variation Generally, variation is used to describe patterns in the data. Seasonal Variation Increasing Variation

14. Time Series: Stability If there are no patterns in the time plot, then it is considered stable. Stability helps us confirm or reject the identically distributed part of iid/random sample. In order for data to be considered stable, both the mean and the variance of the observations needs to be constant over time.

15. Q-Q Plots Checks assumption that observations are from a normally distributed parent population Q stand for quantiles (percentiles): graph compares Quantiles from the standard normal distribution with Quantiles from our sample Want a straight line Better than a histogram

16. Q-Q Plot of Data from an Approximately Normal Distribution

17. Q-Q Plots that do NOT allow us to assume a population with Normal Distribution

18. R scripts Canvas homepage -> R tutorials Open timeseries.rdata or qqplot.rdata – Canvas homepage -> R tutorials ->Time Series/QQ plots Start script with timeseries() or qqplot() – Without the underscore printed in the lab workbook

19. Warm Up

20. Lab With a partner or two, work on the Lab You will not get credit if you work alone Work with employee data.sav If you finish early, complete the Cool Down, R practice, Example Exam Question, or Practice HW problem 3

24. IQR=$13,162.50 IQR=$7,125.00 IQR=$16,200.00

27. Cool Down Everyone turns in own ticket Work on Cool Down in groups

28. iClicker Survey: Students were asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 10, 14, 20, 60 Fill in the blank: About 75% of the students spent at least ___ hours studying in a typical week. A.10 B.14 C.20 D.45

29. iClicker Survey: Students were asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 10, 14, 20, 60 Fill in the blank: About 75% of the students spent at least ___ hours studying in a typical week. A.10 B.14 C.20 D.45

30. iClicker Survey: Students were asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 10, 14, 20, 60 What percent of students reported studying between 10 and 20 hours in a typical week? A.68% B.50% C.25% D.75%

31. iClicker Survey: Students were asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 10, 14, 20, 60 What percent of students reported studying between 10 and 20 hours in a typical week? A.68% B.50% C.25% D.75%

32. iClicker Which of the following provides the most information about the shape of a data set? A.Boxplot B.Pie chart C.Five number summary D.Histogram

33. iClicker Which of the following provides the most information about the shape of a data set? A.Boxplot B.Pie chart C.Five number summary D.Histogram

34. iClicker Here is a graph showing revenue for a company. What kind of graph is this? A. Bar chart B. Histogram C. Time plot D. Box plot

35. iClicker Here is a graph showing revenue for a company. What kind of graph is this? A. Bar chart B. Histogram C. Time plot D. Box plot

36. iClicker Cost of a gallon of gas Can we describe this graph as… A. Right Skewed B. Left Skewed C. Neither

37. iClicker Cost of a gallon of gas Can we describe this graph as… A. Right Skewed B. Left Skewed C. Neither

38. iClicker In a boxplot, what does a dot represent? A.Quartile B.Mean C.Median D.Mode E.Outlier

39. iClicker In a boxplot, what does a dot represent? A.Quartile B.Mean C.Median D.Mode E.Outlier

40. iClicker Which time plot is the most stable? A. B. C.

41. iClicker Which time plot is the most stable? A. B. C.

42. iClicker How do you feel about the material covered today? A.Completely understood everything B.Understood main ideas, shaky on details C.Good for the first half, lost for the second D.Had trouble with some main ideas E.Difficulty following most materials

44. Reminders Good job setting up LectureBook Practice Homework due Thursday 8 am Pre-lab 3 due Monday 8 am Office Hours Food Allergies?