ࡱ>  bjbjVV 8v<<mvIIVVVVVWWW8IWLWW%$X+YAYAYAY\p]$5]IVaa\a\@aaVVAYAY fffalVAYVAYfaffbpTAY`-#W)c| V0%v}c8}TT}V,I],u^fK__I]I]I]eI]I]I]%aaaa}I]I]I]I]I]I]I]I]I]I U:  Lesson 4.1 Statistics Concepts Engineers use statistics to make informed decisions based upon established principles. Visual representations of data analyses allow for easy distribution and understanding of data. Statistics is based upon both theoretical and experimental data analysis. Performance Objectives It is expected that students will: Calculate the theoretical probability that an event will occur. Calculate the experimental frequency distribution of an event occurring. Apply the Bernoulli process to events that only have two distinct possible outcomes. Apply AND, OR, and NOT logic to probability. Apply Bayes theorem to calculate the probability of multiple events occurring. Create a histogram to illustrate frequency distribution. Calculate the central tendency of a data array, including mean, median, and mode. Calculate data variation, including range, standard deviation, and variance. Essential Questions Why is it crucial for designers and engineers to utilize statistics throughout the design process? Why is process control a necessary statistical process for ensuring product success? Why is theory-based data interpretation valuable in decision making? Why is experiment-based data interpretation valuable in decision making? Key Terms AccuracyDegree of conformity of a measure to a standard value.Bar CharCategorical data graphBayes TheoremThe probability of an event occurring based upon other event probabilitiesData Numbers or information describing some characteristic.Data VariationMeasure of data scatterDeviationAmount of difference between a value and the mean.ExperimentAn activity with observable results.EventA subset of a sample space.Frequency DistributionListing of data values along with their corresponding frequencies.Frequency PolygonsFrequency distribution graphHistogramFrequency distribution graphMean Arithmetic averageMean DeviationMeasure of variation equal to the sum of the deviations of each value from the mean.MedianMiddle value of a set of values arranged in order of magnitude.ModeThe value that occurs most frequently.Normal DistributionBell-shaped probability distribution.OutcomeThe result of an experiment.Pie ChartCategorical data graph %ProbabilityThe calculated likelihood that a given event will occur.Process ControlTo monitor and control a process so that the quality of the output/product improves.Qualitative DataValues that possess names or labelsQuantitative DataValues that represent a measurable quantityQuality AssuranceThe use of quality control techniques associated with a process.ReliabilityThe probability of satisfactory operation of the product in a given environment over a specified time interval.Sample SpaceA set of all possible outcomes or events in an experiment that cannot be further broken down.Standard DeviationThe square root of the variance.StatisticsThe collection, evaluation, and interpretation of dataStatistical Process ControlSPC is a method of monitoring, controlling, and ideally improving a process through statistical analysis. Its four basic steps include measuring the process, eliminating variances in the process to make it consistent, monitoring the process, and improving the process to its best target value.ToleranceThe difference between the maximum and minimum dimensions allowed within the design of a product.VarianceThe difference between samples. Instructional Resources Presentations HYPERLINK "C:\\Documents and Settings\\012291\\Local Settings\\Temporary Internet Files\\Content.IE5\\PowerPoints\\Probability.ppt"Probability HYPERLINK "C:\\Documents and Settings\\012291\\Local Settings\\Temporary Internet Files\\Content.IE5\\PowerPoints\\Statistics.ppt"Statistics Word Documents HYPERLINK "C:\\Documents and Settings\\012291\\Local Settings\\Temporary Internet Files\\Content.IE5\\YMG6ENJ1\\Activities\\CareerReflectionAbstractPresentation.doc"Career Reflection, Abstract, and Presentation HYPERLINK "C:\\Documents and Settings\\012291\\Local Settings\\Temporary Internet Files\\Content.IE5\\YMG6ENJ1\\Activities\\A4_1_1Statistical Data Exploration.doc"Activity 4.1.1 Statistical Data Exploration HYPERLINK "C:\\Documents and Settings\\012291\\Local Settings\\Temporary Internet Files\\Content.IE5\\YMG6ENJ1\\Activities\\A4_1_2CandyStatistics.doc"Activity 4.1.2 Candy Statistics HYPERLINK "C:\\Documents and Settings\\012291\\Local Settings\\Temporary Internet Files\\Content.IE5\\YMG6ENJ1\\Activities\\A4_1_3ControlCharts.doc"C:\Documents and Settings\012291\Local Settings\Temporary Internet Files\Content.IE5\YMG6ENJ1\Activities\A4_1_3ControlCharts.docHYPERLINK "C:\\Documents and Settings\\012291\\Local Settings\\Temporary Internet Files\\Content.IE5\\YMG6ENJ1\\Activities\\L4_1KeyTermCrossword.doc"Lesson 4.1 Key Terms Crossword Reference Sources Coolidge, F. (2006). Statistics: A gentle introduction. Thousand Oaks, CA: Sage. International Technology Education Association. (2000). Standards for technological literacy. Reston, VA: ITEA. National Council of Teachers of English (NCTE) and International Reading Association (IRA) (1996). Standards for the English language arts. Newark, DE: IRA; Urbana, IL: NCTE. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author. National Research Council (NRC). (1996). National science education standards. Washington, D. C.: National Academy Press. TAN. (2000). Finite mathematics. Pacific Grove, CA: Brooks/Cole. Triola, M. (2005). Elementary statistics. New York, NY: Pearson. Woodbury, G. (2002). Introduction to statistics. Pacific Grove, CA: Duxbury.      Project Lead The Way, Inc. 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