Probability and Statistics

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# Probability and Statistics - PowerPoint PPT Presentation

Probability and Statistics. ECI 695 February 19, 2009 Day 6. Week 5 Homework. Read DMI Chapter 5 Video: Woodpecker Habitat Math Activity: Median as a Tool in Data Description Reading: Stem and Leaf Plots in the Primary Grades Reading: NCTM Yearbook Chapters 1 and 2 Project 1: Feb 26.

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### Probability and Statistics

ECI 695

February 19, 2009

Day 6

Week 5 Homework
• Read DMI Chapter 5
• Video: Woodpecker Habitat
• Math Activity: Median as a Tool in Data Description
• Reading: Stem and Leaf Plots in the Primary Grades
• Reading: NCTM Yearbook Chapters 1 and 2
• Project 1: Feb 26
Steckroth Website
• http://www.odu.edu/~jsteckro/
• Check this site for additional documents until Blackboard is operational
Week 6 Agenda
• Read DMI Chapter 5
• Video: Woodpecker Habitat
• Math Activity: Median as a Tool in Data Description
• Reading: Stem and Leaf Plots in the Primary Grades
• Reading: NCTM Yearbook Chapters 1 and 2
Question 2
• Describe and compare the four sets of data. Are the four grades similar? Different?
Grade 2 n = 20

Median = (8 + 8)/2 = 8

Grade 2 n = 20

Median = (8 + 8)/2 = 8

Q1 = (8 + 8)/2 = 8

Grade 2 n = 20

Median = (8 + 8)/2 = 8

Q1 = (8 + 8)/2 = 8

Q3 = (10 + 10)/2 = 10

Grade 2 n = 20

Median = (8 + 8)/2 = 8

Minimum = 2

Q1 = (8 + 8)/2 = 8

Maximum = 13

Q3 = (10 + 10)/2 = 10

Grade 2 n = 20

2, 8, 8, 10, 13

IQR =

10 - 8 = 2

Outliers?

5NS = 2, 8, 8, 10, 13

IQR = 2

1.5 ( 2 ) = 3

Outliers?

5NS = 2, 8, 8, 10, 13

IQR = 2

MWL = 1.5 ( 2 ) = 3

LF = LQ - MWL = 8 - 3 = 5

UF = UQ + MWL = 10 + 3 = 13

Question 3
• If just the mode for each grade were reported to you, what would that tell you about the data?
• What wouldn’t you be able to tell?
Question 4
• Find the median number of teeth lost for each grade. If just the median for each grade were reported to you, how would that help you compare the grade levels?
Question 5
• Complete for Homework

### Teeth Video

Statistical Investigation

Question

Collect Data

Analyze

Interpret

Communicate

This endangered woodpecker is found in old, open pine forests. Creates nest cavities in living pine trees. Holes for pine resin to ooze are created in cavity trees to prevent snakes from climbing the tree. Males have a small red patch of feathers located near the ear (or cockade), which is rarely seen in the field. Also called RCW, this species is about the size of an eastern bluebird (8 1/2”).

### Woodpecker Habitat

Probability and Sampling

Mathematical Topics
• Sampling
• With replacement
• Without replacement
• Collecting data
• Representing data
• Making Predictions
• Reliability of samples
• Use of calculators

### SIMULATION

Emerging Mathematical Abilities
• Comprehending one-to-one correspondence
• Understanding set membership
• Retrieving information
• Creating order
Goal
• Support children’s use of mathematical reasoning as they move from collecting to interpreting data.
Professional Development
• What are children capable of doing?
• How do you talk with young children?
Graphing through surveys

• Familiar activities
• Interesting to children
• Opportunities for mathematical reasoning
• Cross-content areas
Harold’s Accomplishments
• Posed his own question
• Demonstrated 1-to-1 correspondence
• Displayed several levels of info
• Invented symbols
• Solved a problem (no answer)
• Sought validity
• Organized his recordings into groups
Intention vs. Convention
• “Just because a child’s product may look unconventional on the surface, it does not mean that it lacks intention.”
Concerns
• Graphs must conform to standard formats
• Children must be shown “how”
• Lack of confidence in their ability to collect and organize data
• Fear of how to talk with children about their ideas
Upper Elementary:Summarizing and Comparing
• Data as “aggregate” (Konold)
• Shape, spread, concentration
• Mean and standard deviation; median and quartiles
• Median: elementary
• Mean: middle school
Transitioning
• Mode
• Clumps
• Measures of Central Tendency
Recommendations
• Have students develop representations
• Meaning of symbols
• Compare groups
• Look for concentrations
• Ask for descriptions of the clumps
Week 6 Homework
• Read DMI Chapter 6
• Math Activity: Stem and Leaf Plots
• Reading: NCTM Yearbook Chapter 3

Learning to Talk Back to a Statistic

• Reading: The Power of Representation

Graphs and Glyphs

• Project 1: Feb 26