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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.

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Probability and statistics

Probability and Statistics

ECI 695

February 19, 2009

Day 6


Week 5 homework
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
Steckroth Website

  • http://www.odu.edu/~jsteckro/

  • Check this site for additional documents until Blackboard is operational


Week 6 agenda
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







Math activity teeth

See Handout

MATH ACTIVITY: TEETH



Ti graphing calculator analysis of grade 1 data
TI Graphing CalculatorAnalysis of Grade 1 Data



Question 2
Question 2

  • Describe and compare the four sets of data. Are the four grades similar? Different?



Grade 2 n 201
Grade 2 n = 20

Median = (8 + 8)/2 = 8


Grade 2 n 202
Grade 2 n = 20

Median = (8 + 8)/2 = 8

Q1 = (8 + 8)/2 = 8


Grade 2 n 203
Grade 2 n = 20

Median = (8 + 8)/2 = 8

Q1 = (8 + 8)/2 = 8

Q3 = (10 + 10)/2 = 10


Grade 2 n 204
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 205
Grade 2 n = 20

2, 8, 8, 10, 13

IQR =

10 - 8 = 2


Outliers
Outliers?

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

IQR = 2

1.5 ( 2 ) = 3


Outliers1
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
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
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
Question 5

  • Complete for Homework




Statistical investigation
Statistical Investigation

Question

Collect Data

Analyze

Interpret

Communicate



Red cockaded woodpecker1
Red-cockaded Woodpecker

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

Woodpecker Habitat

Probability and Sampling


Mathematical topics
Mathematical Topics

  • Sampling

    • With replacement

    • Without replacement

  • Collecting data

  • Representing data

  • Making Predictions

  • Reliability of samples

  • Use of calculators



Graphing with four year olds
GRAPHING WITH FOUR-YEAR-OLDS

Yearbook Chapter 1


Emerging mathematical abilities
Emerging Mathematical Abilities

  • Comprehending one-to-one correspondence

  • Understanding set membership

  • Retrieving information

  • Creating order


Probability and statistics
Goal

  • Support children’s use of mathematical reasoning as they move from collecting to interpreting data.


Professional development
Professional Development

  • What are children capable of doing?

  • How do you talk with young children?


Graphing through surveys
Graphing through surveys

Advantages:

  • Familiar activities

  • Interesting to children

  • Opportunities for mathematical reasoning

  • Cross-content areas



Harold s accomplishments
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
Intention vs. Convention

  • “Just because a child’s product may look unconventional on the surface, it does not mean that it lacks intention.”


Concerns
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





What does it mean that five has a lot
WHAT DOES IT MEAN THAT“FIVE HAS A LOT?”

Yearbook Chapter 2





Upper elementary summarizing and comparing
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
Transitioning

  • Mode

  • Clumps

  • Measures of Central Tendency



Recommendations
Recommendations

  • Have students develop representations

  • Meaning of symbols

  • Compare groups

  • Look for concentrations

  • Ask for descriptions of the clumps


Week 6 homework
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