# SOCR Events July2008

## Contents

- 1 SOCR Events - SOCR Demonstration at the CensusAtSchool International Workshop
- 2 Logistics
- 3 Objectives
- 4 Use basic concepts of probability to determine the likelihood of an event and compare the results of various experiments
- 5 Display and compare data to make predictions and formulate conclusions
- 6 Calculate probabilities of events and compare theoretical and experimental probability
- 7 Formulate questions and answer the questions by organizing and analyzing data
- 8 Summarize, display, and analyze bivariate data
- 9 Apply basic concepts of probability
- 10 Use percentiles and measures of variability to analyze data
- 11 Compute probabilities for discrete distributions and use sampling distributions to calculate approximate probabilities
- 12 Analyze bivariate data using linear regression methods
- 13 References

## SOCR Events - SOCR Demonstration at the CensusAtSchool International Workshop

## Logistics

**Date**: Tue., July 29, 2008, 3:15-4:00 PM.**Presenter**: Ivo Dinov, Statistics Online Computational Resource (SOCR)**Title**:*Using SOCR to motivate simulation experiments in middle and high school***Venue**: Powell Library (CLICC Classroom C, Powell 320C, Powell Building Realtime WebCam, use only the North-West elevator/stairway)**Sponsors**: California CensusAtSchool, UCLA Statistics, C@S, SOCR**Audience**: This presentation is intended for middle and high school teachers in various science and quantitative disciplines.**Overarching Goals**: To present an integrated approach for technology enhanced instruction using free Internet-based resources (web-applets, instructional materials and learning activities)

## Objectives

The specific aims of this hands-on presentation are to discuss the use of the free and integrated Internet-based SOCR Resources for

- Data download and Data Generation
- Virtual Experimentation and Simulation
- Exploratory Data Analysis
- Common Statistical Analyses

## 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

- 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.

## References

- Interactive Statistics Education EBook
- SOCR Home page: http://www.socr.ucla.edu

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