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Probability and Statistics ECI 695 January 22, 2009 Day 2.
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Transcript of Probability and Statistics ECI 695 January 22, 2009 Day 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
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
Steckroth Website
• http://www.odu.edu/~jsteckro/• Check this site for additional documents until
Blackboard is operational
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
Week 1 Vocabulary
• Population vs. Sample• Quantitative vs. Qualitative Data• Variation• Random Error and Bias• Random Sample• Representative Sample
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
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/da
ta/session1/part_h/homework.html
How Long is a Minute Video
• First-grade students• Look for teacher and student actions and
communication• Note specific instances
Problem C1Would 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?
H1: Pine Needles
b. Notice that the 20 pine-needle measurements are not all the same.
What is the source of this variation?
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?
Nickel Activity
• Look at some nickels and see if you can locate the mint mark.
• Record date and mint mark• Report Findings
Nickel Photographs
Date on Coin• 1963• 1977• 1981• 1988• 1994• 1996• 1999• 2004
Mint Mark• None• None• D• D• P• P• P• P
Nickel Videoa) 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.
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
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
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.
Example
• What is your favorite snack food?• Answers: popcorn, pudding, fruit, jello,
cheese and crackers, ice cream, peanuts, potato chips, popcorn
• Categories?
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
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.
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?
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
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
Raisins
• Question: How many raisins are in a ½ ounce box of raisins?
• Collect data• Display data in a line plot
Making a Frequency Table
• Take the line plot data representation and show the same information in a table
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 ?
Frequency Bar Graphs
• Three stages from Line Plot to Bar Graph– Line Plot– Dots and Rectangles– Frequency Bar Graph
Summary
• Data Organization and Representation– Patterns in Data– Line Plots– Frequency Tables– The Median– Bar Graphs and Relative Frequencies
• Homework
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)