TEKS: Chapter 111. Mathematics See All Teacher Resources

111.44.c.4

(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. The student is expected to:

• (A) use a two-way frequency table as a sample space to identify whether two events are independent and to interpret the results;

• (B) use the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), in mathematical and real-world problems;

• (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.