| (C) calculate conditional probabilities and probabilities
of compound events using tree diagrams, Venn diagrams, area models,
and formulas;
(D) interpret conditional probabilities and probabilities
of compound events by analyzing representations to make decisions
in problem situations;
(E) use probabilities to make and justify decisions
about risks in everyday life;
(F) calculate expected value to analyze mathematical
fairness, payoff, and risk;
(G) determine the validity of logical arguments that
include compound conditional statements by constructing truth tables;
(H) identify limitations and lack of relevant information
in studies reporting statistical information, especially when studies
are reported in condensed form;
(I) interpret and compare statistical results using
appropriate technology given a margin of error;
(J) identify 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;
(K) describe 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;
(L) determine 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;
(M) identify the population of interest for a statistical
investigation, select an appropriate sampling technique, and collect
data;
(N) identify the variables to be used in a study;
(O) determine possible sources of statistical bias
in a study and how bias may affect the validity of the results;
(P) create data displays for given data sets to investigate,
compare, and estimate center, shape, spread, and unusual features
of the data;
(Q) analyze possible sources of data variability, including
those that can be controlled and those that cannot be controlled;
(R) report 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;
(S) justify the design and the conclusion(s) of statistical
studies, including the methods used; and
(T) communicate statistical results in oral and written
formats using appropriate statistical and nontechnical language.
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