Download Data Analysis, Probability, and Statistics for Teachers

Data Analysis, Probability, and Statistics for Teachers
Jim Albert
Department of Mathematics and Statistics, Bowling Green State University
[email protected]
This book (to be published by Key College Publishing in late 2006) is a data analysis and probability
textbook for prospective and in-service Middle School and High School teachers. The National Council of
Teachers in Mathematics (NCTM) has recently established standards in data analysis and probability to
be taught to all students from grades K-12. This text is designed to teach the prospective teachers basic
concepts in probability and statistics so they have the background to teach the content listed in the NCTM
standards. The basic concepts in data analysis and probability will be taught by means of discovery and
group interaction on directed activities, both of the hands-on and technology varieties. Technology is
implemented by means of the software Fathom, Tinkerplots and the TI 84-Plus graphing calculator.
TABLE OF CONTENTS
DATA ANALYSIS
Topic D1: Statistics, data, and variables
TOPICS
Statistics and data
Reading articles in the media
ACTIVITIES
ACTIVITY: Getting to know you
ACTIVITY: Meet the states data
Topic D2: Graphing data
TOPICS
Graphing categorical data
Graphing measurement data
Stemplot
Histogram
Experimenting with different graphs
ACTIVITIES
ACTIVITY: The shape of the data
ACTIVITY: Matching variables and shapes
Topic D3: Summaries of data
TOPICS
Summarizing categorical data
Deviations and the mean
Comparing the median and the mean
Measures of spread
The standard deviation
Interpreting s: the 68/95/99.7 rule for bell-shaped
data
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ACTIVITIES
TINKERPLOTS ACTIVITY: Introduction to
Tinkerplots
INTERNET ACTIVITY: Collecting some data on
cities
ACTIVITY: Measurement bias
ACTIVITY: Matching statistics to graphs
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Topic D4: Comparing batches
TOPICS
Comparison of batches of categorical data
Comparison of batches of measurement data
ACTIVITIES
ACTIVITY: Let us count
Topic D5: An Introduction to Relationships
TOPICS
Different ways of relating two variables
Scatterplots
ACTIVITIES
TINKERPLOTS ACTIVITY: Studying relationships
Topic D6: Summarizing Relationships
TOPICS
Correlation coefficient
Least-squares line
The median-median line – a robust alternative of
fitting a line
ACTIVITIES
ACTIVITY: Matching correlations with scatterplots
FATHOM ACTIVITY: Guessing correlations
ACTIVITY: Fitting a line by eye to Galton’s data
FATHOM ACTIVITY: Fitting a “best” line
FATHOM ACTIVITY: Exploring some Olympics
data
ACTIVITY: Regression to the mean
Topic D7: Relationships between categorical variables
TOPICS
Describing association in a two-way table
ACTIVITIES
ACTIVITY: Predictable pairs
COLLECTING DATA
TOPICS
Random sampling
Designed experiments
ACTIVITIES
ACTIVITY: Random rectangles
ACTIVITY: Jumping frogs
PROBABILITY
Topic P1: Probability – a measure of uncertainty
TOPICS
The classical (equally likely) view of a probability
The frequency view of a probability
The subjective view of a probability
ACTIVITIES
ACTIVITY: Tossing and spinning a poker chip
ACTIVITY: A calibration experiment
Topic P2: Sample space
TOPICS
Different representations of a sample space
Assigning probabilities
A more formal look at probability
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ACTIVITIES
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Topic P3: Let me count the ways
TOPICS
Arrangements
Combinations
Arrangements of non-distinct objects
Playing Yahtzee
ACTIVITIES
ACTIVITY: Mothers and babies
ACTIVITY: Sampling from a bag
Topic P4: Computing probabilities by simulation
TOPICS
Simulating a lottery game
Basic components of a simulation experiment
The collector’s problem
ACTIVITIES
FATHOM ACTIVITY: Mixed-up letters
FATHOM ACTIVITY: Hanging over a gorge
FATHOM OR TI-84 PLUS ACTIVITY: The longest
run
FATHOM OR TI-84 PLUS ACTIVITY: Sampling
people from a room
FATHOM OR TI-84 PLUS ACTIVITY: The birthday
problem
Topic P5: Conditional Probability
TOPICS
Reduced sample space
Conditional probability in everyday life
Conditional probability in a two-way table
Conditional probability and multiplying probabilities
ACTIVITIES
FATHOM ACTIVITY: Rolling two dice
Topic P6: Probability distributions
TOPICS
Constructing a probability distribution
Expected value
Standard deviation
Empirical rule
ACTIVITIES
ACTIVITY: Investing money
FATHOM ACTIVITY: Throwing two four-sided dice
FATHOM ACTIVITY: Constructing a probability
distribution by simulation
FATHOM ACTIVITY: Playing roulette
Topic P7: Coin tossing distributions
TOPICS
Binomial, Geometric distributions
ACTIVITIES
ACTIVITY: Coin flipping
FATHOM ACTIVITY: A streaky coin
Topic P8: Continuous distributions
TOPICS
The uniform distribution
A probability density
The probability function (the cdf F(x))
ACTIVITIES
FATHOM ACTIVITY: Spinning away
FATHOM ACTIVITY: Waiting for the shuttle
FATHOM ACTIVITY: A test with a bimodal
distribution
Summarizing a continuous random variable
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Topic P9: The Normal distribution
TOPICS
Computing normal probabilities
Percentiles
Binomial probabilities and the normal curve
Sampling distribution of the mean
ACTIVITIES
FATHOM ACTIVITY: Sampling heights
FATHOM ACTIVITY: Rolling biased dice
Topic P10: Introduction to Statistical Inference
TOPICS
Population, sample, parameter, statistic
Sampling distribution of a proportion
Estimating with confidence
Estimating a population mean
Testing hypotheses – p –values
ACTIVITIES
(Copyright: Key College Publishing)
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