Probability and Statistics

ECI 695January 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

STATISTICS AS PROBLEM SOLVINGAnnenberg Session 1

Four Step Process

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

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

SIMULATIONS

Simulations

• How Long is a Minute• Measurement Bias• Random Sampling

How Long is a Minute?

• Results from our class

How Long is a Minute Video

• First-grade students• Look for teacher and student actions and

communication• Note specific instances

Measurement Bias

Measurement Bias

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?

Bias in Measurement

Random Sampling

H1, H2, H3

H1: Pine Needles

a. Think of a question that collecting this data might answer.

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?

H2: Nickels

Nickel Investigation

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

Sort the Data

• Spreadsheet

Homework Data

• Any observations?

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.

H3: Pulse Rate

• Sources of variation?

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

GETTING STARTED WITH DATADMI Working with Data, Chapter 1

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?

Your Question

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

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

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?

Focus Questions

• Homework for Week 2

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

DATA ORGANIZATION AND REPRESENTATION

Annenberg Session 2

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

PATTERNS IN VARIATIONAnnenberg Part A

Patterns in Variation

• Family Size• Coin characteristics

LINE PLOTSAnnenberg Part B

Raisins

• Question: How many raisins are in a ½ ounce box of raisins?

• Collect data• Display data in a line plot

Pool Our Data

• Eastern Shore• TCCP

Line Plot

• Document camera

Answer?

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

Line Plot

FREQUENCY TABLESAnnenberg Part C

Making a Frequency Table

• Take the line plot data representation and show the same information in a table

Frequency Table

Cumulative Frequency Table

• Show the raisin data as cumulative frequencies.

Cumulative Frequency Table

• Show the raisin data as cumulative frequencies.

PSAT Cumulative Frequency

Intervals and Ranges

• Use the cumulative frequency table to answer interval questions

THE MEDIANAnnenberg Part D

The Median

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

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 ?

BAR GRAPHS AND RELATIVE FREQUENCIES

Annenberg Part E

Frequency Bar Graphs

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

Beginning Stage

Intermediate Stage

Final Stage

Relative Frequency

Fractions, Decimals, Percentages

Relative Frequency Bar Graph

Relative Frequency Bar Graph

SUMMARY: SESSION 2

Summary

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

• Homework

HOMEWORK FOR WEEK 2

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)

Questions?