SOCR Events May2008

Logistics

• Title: Interactive Web-based Probability and Statistics using SOCR
• Date: Monday, May 05, 2008, 2:00-2:30 PM (Pacific Time)
• Presenter: Ivo Dinov, Statistics Online Computational Resource (SOCR)
• Venue: This webinar is presented as part of the follow-up activities for the American Statistical Association's Meeting Within a Meeting workshop for math and science teachers. If you are not a Meeting Within a Meeting participant and are interested in viewing the live webinar, please contact Rebecca Nichols (Rebecca@amstat.org).
• Webinar Archive: The complete record of this webinar will be posted online in May 2008.
• Sponsors: ASA, GAISE, MWM, SOCR
• Audience: This Webinar is intended for middle school teachers in various science and quantitative disciplines.
• Overarching Goals: To present an integrated approach for IT technology blended instruction using free Internet-based resources (web-applets, instructional materials and learning activities)

Objectives

Use basic concepts of probability to determine the likelihood of an event and compare the results of various experiments

• Write the results of a probability experiment as a fraction, ratio, or decimal, between zero and one, or as a percent between zero and one hundred, inclusive

• Compare experimental results with theoretical probability

• Compare individual, small group, and large group results of a probability experiment

Display and compare data to make predictions and formulate conclusions

• Display data using tables, scatter plots, and circle graphs

• Compare two similar sets of data on the same graph

• Compare two different kinds of graphs representing the same set of data

• Propose and justify inferences and predictions based on data

Calculate probabilities of events and compare theoretical and experimental probability

Use of the Fundamental Counting Principle, complement, theoretical probability, experiment, data, percentile, histogram, box-and-whisker plot, spread

• Elementary Probability Example: Each of the three boxes below contains two types of balls (Red and Green). Box 1 has 4 Red and 3 Green balls, box 2 has 3 Red and 2 Green balls, and box 3 has 2 Red and 1 Green balls. All balls are identical except for their labels. Which of the three boxes are you most likely to draw a Red ball from? In other words, if a randomly drawn ball is known to be Red, which box is the one that we most likely drew the ball out of?

• Solve counting problems using the Fundamental Counting Principle

• Calculate the probability of an event or sequence of events with and without replacement using models

• Recognize that the sum of the probability of an event and the probability of its complement is equal to one

• Make approximate predictions using theoretical probability and proportions

• Collect and interpret data to show that as the number of trials increases, experimental probability approaches the theoretical probability

Formulate questions and answer the questions by organizing and analyzing data

• Formulate questions that can be answered through data collection and analysis

• Determine the 25^th and 75^th percentiles (first and third quartiles) to obtain information about the spread of data

• Graphically summarize data of a single variable using histograms and box-and-whisker plots

• Compute the mean and median of a numerical characteristic and relate these values to the histogram of the data

• Use graphical representations and numerical summaries to answer questions and interpret data

Summarize, display, and analyze bivariate data

Use of scatter plot, positive correlation, negative correlation, no correlation, line of best fit, bivariate data.

• Collect, record, organize, and display a set of data with at least two variables

• Determine whether the relationship between two variables is approximately linear or nonlinear by examination of a scatter plot

• Characterize the relationship between two linear related variables as having positive, negative, or approximately zero correlation

• Estimate, interpret, and use lines fit to bivariate data

• Estimate the equation of a line of best fit to make and test conjectures

• Interpret the slope and y-intercept of a line through data

• Predict y-values for given x-values when appropriate using a line fitted to bivariate numerical data

Apply basic concepts of probability

Use of permutation, combination, conditional probability, discrete random variable, standard deviation, interquartile range, percentile.

• Distinguish between permutations and combinations and identify situations in which each is appropriate

• Calculate probabilities using permutations and combinations to count events

• Compute conditional and unconditional probabilities in various ways, including by definitions, the general multiplication rule, and probability trees

• Define simple discrete random variables

Use percentiles and measures of variability to analyze data

• Compute different measures of spread, including the range, standard deviation, and interquartile range

• Compare the effectiveness of different measures of spread, including the range, standard deviation, and interquartile range in specific situations

• Use percentiles to summarize the distribution of a numerical variable

• Use histograms to obtain percentiles

Compute probabilities for discrete distributions and use sampling distributions to calculate approximate probabilities

• Obtain sample spaces and probability distributions for simple discrete random variables.

• Compute binomial probabilities using Pascal’s Triangle and the Binomial Theorem.

• Compute means and variances of discrete random variables.

• Compute probabilities using areas under the Normal Curve.

• Calculate parameters of sampling distributions for the sample average, sum, and proportion.

• Calculate probabilities in real problems using sampling distributions.

Analyze bivariate data using linear regression methods

• Fit regression lines to pairs of numeric variables and calculate the means and standard deviations of the two variables and the correlation coefficient, using technology.

• Compute predictions of y-values for given x-values using a regression equation, and recognize the limitations of such predictions.

• Compute and use the standard error for regression.

References

• Utah Secondary Core Curriculum Standards for Statistics
• (GAISE) Report: A Pre-K -12 Curriculum Framework
• Interactive Statistics Education EBook
• SOCR Home page: http://www.socr.ucla.edu

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