AQR.4

Probabilistic and statistical reasoning. The student uses the process standards in mathematics to generate new understandings of probability and statistics. The student analyzes statistical information and evaluates risk and return to connect mathematical ideas and make informed decisions. The student applies a problem-solving model and statistical methods to design and conduct a study that addresses one or more particular question(s). The student uses multiple representations to communicate effectively the results of student-generated statistical studies and the critical analysis of published statistical studies.

AQR.4.AUse a two-way frequency table as a sample space to identify whether two events are independent and to interpret the results.AQR.4.BUse the Addition Rule, P(A or B)= P.A+ P.B- P(A and B), in mathematical and real-world problems.AQR.4.CCalculate conditional probabilities and probabilities of compound events using tree diagrams, Venn diagrams, area models, and formulas.AQR.4.DInterpret conditional probabilities and probabilities of compound events by analyzing representations to make decisions in problem situations.AQR.4.EUse probabilities to make and justify decisions about risks in everyday life.AQR.4.FCalculate expected value to analyze mathematical fairness, payoff, and risk.AQR.4.GDetermine the validity of logical arguments that include compound conditional statements by constructing truth tables.AQR.4.HIdentify limitations and lack of relevant information in studies reporting statistical information, especially when studies are reported in condensed form.AQR.4.IInterpret and compare statistical results using appropriate technology given a margin of error.AQR.4.JIdentify potential misuses of statistics to justify particular conclusions, including assertions of a cause-and-effect relationship rather than an association, and missteps or fallacies in logical reasoning.AQR.4.KDescribe strengths and weaknesses of sampling techniques, data and graphical displays, and interpretations of summary statistics and other results appearing in a study, including reports published in the media.AQR.4.LDetermine the need for and purpose of a statistical investigation and what type of statistical analysis can be used to answer a specific question or set of questions.AQR.4.MIdentify the population of interest for a statistical investigation, select an appropriate sampling technique, and collect data.AQR.4.NIdentify the variables to be used in a study.AQR.4.ODetermine possible sources of statistical bias in a study and how bias may affect the validity of the results.AQR.4.PCreate data displays for given data sets to investigate, compare, and estimate center, shape, spread, and unusual features of the data.AQR.4.QAnalyze possible sources of data variability, including those that can be controlled and those that cannot be controlled.AQR.4.RReport results of statistical studies to a particular audience, including selecting an appropriate presentation format, creating graphical data displays, and interpreting results in terms of the question studied.AQR.4.SJustify the design and the conclusion(s) of statistical studies, including the methods used.AQR.4.TCommunicate statistical results in oral and written formats using appropriate statistical and nontechnical language.
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