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Probability and Statistics

Probability and Statistics

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Probability and Statistics

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

  2. Housekeeping Chores • Registration Fax: 757-686-6219. • 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. Emails and Website • Sent by email 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 • http://www.odu.edu/~jsteckro/ • 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. Annenberg Session 1 Statistics as problem solving

  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 • http://www.learner.org/courses/learningmath/data/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. Measurement Bias

  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 None D D P P P P • 1963 • 1977 • 1981 • 1988 • 1994 • 1996 • 1999 • 2004

  29. Sort the Data • Spreadsheet

  30. Homework Data • Any observations?

  31. Nickel Video • There are differences in the mint locations. What is the source of this variation? • There are differences in the mint years. What is the source of this variation? • What observations can you make about this data? For example, which location appears most frequently? Which decade? • When were the coins with no mint location minted? Does this suggest any new statistical questions? • Record the mint locations and years for 10 of your own nickels. How do your data compare to the data recorded above? • 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.

  32. H3: Pulse Rate • Sources of variation?

  33. 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

  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. DMI Working with Data, Chapter 1 Getting started with data

  36. 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.

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

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

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

  40. Focus questions

  41. Focus Questions: Chapter 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.

  42. 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?

  43. Focus Questions • Homework for Week 2

  44. 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

  45. Annenberg Session 2 Data organization and representation

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

  47. Annenberg Part A Patterns in variation

  48. Patterns in Variation • Family Size • Coin characteristics

  49. Annenberg Part B Line plots