# SOCR Events May2008

## Contents

- 1 SOCR Events - SOCR ASA MWM Webinar - Interactive Web-based Probability and Statistics using SOCR
- 2 Logistics
- 3 Objectives
- 3.1 Use basic concepts of probability to determine the likelihood of an event and compare the results of various experiments
- 3.2 Display and compare data to make predictions and formulate conclusions
- 3.3 Calculate probabilities of events and compare theoretical and experimental probability
- 3.4 Formulate questions and answer the questions by organizing and analyzing data
- 3.5 Summarize, display, and analyze bivariate data
- 3.6 Apply basic concepts of probability
- 3.7 Use percentiles and measures of variability to analyze data
- 3.8 Compute probabilities for discrete distributions and use sampling distributions to calculate approximate probabilities
- 3.9 Analyze bivariate data using linear regression methods

- 4 References

## SOCR Events - SOCR ASA MWM Webinar - Interactive Web-based Probability and Statistics using SOCR

## 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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