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Probability and Statistics ECI 695 January 22, 2009 Day 2.

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Presentation on theme: "Probability and Statistics ECI 695 January 22, 2009 Day 2."— Presentation transcript:

1 Probability and Statistics ECI 695 January 22, 2009 Day 2

2 Housekeeping Chores Registration Fax: – Attention Barry Smith – Course Registration Form – Application for Non-Degree Entry – Application for In-State Tuition Books and Materials – NCTM Yearbook – Working with Data

3 s and Website Sent by this past week: Posted on Instructor Website: – Homework for Week 1 – Working with Data Chapters 1 and 2 – Syllabus – PowerPoint slides from Week 1 Pdf format PPt format

4 Steckroth Website Check this site for additional documents until Blackboard is operational

5 Tonight’s Agenda Statistics as Problem Solving Homework for Week 1 – Simulations Working with Data, Chapter 1 – Getting Started with Data Annenberg Session 2 – Data Organization and Representation

6 STATISTICS AS PROBLEM SOLVING Annenberg Session 1

7 Four Step Process

8 Week 1 Vocabulary Population vs. Sample Quantitative vs. Qualitative Data Variation Random Error and Bias Random Sample Representative Sample

9 Tonight’s Agenda Statistics as Problem Solving Homework for Week 1 – Simulations Working with Data, Chapter 1 – Getting Started with Data Annenberg Session 2 – Data Organization and Representation

10 HOMEWORK FOR WEEK 1

11 Homework for Week 1 Learner.org Simulations – How Long is a Minute – Testing Your Measurement Bias – Bias in Sampling: Random Sampling H1, H2, H3 – a/session1/part_h/homework.html a/session1/part_h/homework.html

12 SIMULATIONS

13 Simulations How Long is a Minute Measurement Bias Random Sampling

14 How Long is a Minute? Results from our class

15 How Long is a Minute Video First-grade students Look for teacher and student actions and communication Note specific instances

16 Measurement Bias

17

18 Problem C1 Would you say that the errors you made in the visual judgments of the Interactive Activity were due to random error, or to bias? Why or why not?

19 Bias in Measurement

20 Random Sampling

21 H1, H2, H3

22 H1: Pine Needles a. Think of a question that collecting this data might answer.

23 H1: Pine Needles b. Notice that the 20 pine-needle measurements are not all the same. What is the source of this variation?

24 H1: Pine Needles c. If you have access to some pine needles, measure the length (to the nearest millimeter) of 10 different needles with a metric ruler. If you do not have access to pine needles, measure the length (to the nearest millimeter) of 10 different pieces of spaghetti with a metric ruler. Are the lengths the same?

25 H2: Nickels

26 Nickel Investigation

27 Nickel Activity Look at some nickels and see if you can locate the mint mark. Record date and mint mark Report Findings

28 Nickel Photographs Date on Coin Mint Mark None D D P P P P

29

30 Sort the Data Spreadsheet

31 Homework Data Any observations?

32 Nickel Video a)There are differences in the mint locations. What is the source of this variation? b)There are differences in the mint years. What is the source of this variation? c)What observations can you make about this data? For example, which location appears most frequently? Which decade? d)When were the coins with no mint location minted? Does this suggest any new statistical questions? e)Record the mint locations and years for 10 of your own nickels. How do your data compare to the data recorded above? f)Suppose you knew that the coins with no given mint location were in fact minted in either Philadelphia, Denver, or San Francisco. Can you pinpoint where these coins were minted? Defend your answer, using the data in this problem.

33 H3: Pulse Rate Sources of variation?

34 Tonight’s Agenda Statistics as Problem Solving: recap Homework for Week 1 Working with Data, Chapter 1 – Getting Started with Data Annenberg Session 2 – Data Organization and Representation

35 Tonight’s Agenda Statistics as Problem Solving: recap Homework for Week 1 Working with Data, Chapter 1 – Getting Started with Data Annenberg Session 2 – Data Organization and Representation

36 GETTING STARTED WITH DATA DMI Working with Data, Chapter 1

37 Math Activity: A Data Investigation Work in groups of 3. Answer the question individually. Collect answers from everyone at your site. Analyze the responses in your group. Sort the data in two different ways, each containing at least 3 categories.

38 Example What is your favorite snack food? Answers:popcorn, pudding, fruit, jello, cheese and crackers, ice cream, peanuts, potato chips, popcorn Categories?

39 Your Question With what well-known person would you most like to have a conversation?

40 The List of Well-Known Persons Eastern Shore Barack Obama (3) Bob Seger George Strait Thomas Jefferson Walter Chronkite Warren Buffett Oprah Winfrey Tri-Cities Keon Lindsey (2) Jesus Christ George W. Bush Michelle Obama Mother Theresa Einstein Oprah Winfrey

41 FOCUS QUESTIONS

42 Focus Questions: Chapter 1 1.Look through Alexandra’s and Beverly’s cases. Identify by line number, statements made by at least 5 different children that you think bring up important ideas or issues about collecting, representing, or describing data.

43 Case 3 Olivia 2. In Olivia’s case 3, consider the data about family size: Write down a few statements that describe the data. What are the most important features of this data set?

44 Focus Questions Homework for Week 2

45 Tonight’s Agenda Statistics as Problem Solving: recap Homework for Week 1 Raisins Working with Data, Chapter 1 – Getting Started with Data Annenberg Session 2 – Data Organization and Representation

46 DATA ORGANIZATION AND REPRESENTATION Annenberg Session 2

47 Session 2 Vocabulary cumulative frequency Table discrete data Distribution Frequency frequency bar graph frequency table Interval line plot Median Mode relative frequency relative frequency bar graph

48 PATTERNS IN VARIATION Annenberg Part A

49 Patterns in Variation Family Size Coin characteristics

50 LINE PLOTS Annenberg Part B

51 Raisins Question: How many raisins are in a ½ ounce box of raisins? Collect data Display data in a line plot

52 Pool Our Data Eastern Shore TCCP

53 Line Plot Document camera

54 Answer? What is the answer to the question, “how many raisins are in a ½ ounce box of raisins?

55 Line Plot

56 FREQUENCY TABLES Annenberg Part C

57 Making a Frequency Table Take the line plot data representation and show the same information in a table

58 Frequency Table

59 Cumulative Frequency Table Show the raisin data as cumulative frequencies.

60 Cumulative Frequency Table Show the raisin data as cumulative frequencies.

61 PSAT Cumulative Frequency

62 Intervals and Ranges Use the cumulative frequency table to answer interval questions

63 THE MEDIAN Annenberg Part D

64 The Median From the list of data From a line plot Median Gizmo (ExploreLearning.com)

65 Mathematics: Question 34 11, 2, x, 7, 12 The average (arithmetic mean) of the five numbers above is the same as the median of these numbers. What is one possible value of x ?

66 BAR GRAPHS AND RELATIVE FREQUENCIES Annenberg Part E

67 Frequency Bar Graphs Three stages from Line Plot to Bar Graph – Line Plot – Dots and Rectangles – Frequency Bar Graph

68 Beginning Stage

69 Intermediate Stage

70 Final Stage

71 Relative Frequency

72 Fractions, Decimals, Percentages

73 Relative Frequency Bar Graph

74 SUMMARY: SESSION 2

75 Summary Data Organization and Representation – Patterns in Data – Line Plots – Frequency Tables – The Median – Bar Graphs and Relative Frequencies Homework

76 HOMEWORK FOR WEEK 2

77 Homework for Week 2 Learner.org Session 2 Simulations Solve the Session 2 Problems H1—H5 Read Casebook Chapter 2 – Designing a Data Investigation Answer Focus Questions – Chapter 1 and Chapter 2 Bring measuring tape (cloth)

78 Questions?


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