Texas: Statistics Math Standards
37 standards · 6 domains
STATISTICAL PROCESS SAMPLING AND EXPERIMENTATION. THE STUDENT APPLIES MATHEMATICAL PROCESSES TO APPLY UNDERSTANDINGS ABOUT STATISTICAL STUDIES, SURVEYS, AND EXPERIMENTS TO DESIGN AND CONDUCT A STUDY AND USE GRAPHICAL, NUMERICAL, AND ANALYTICAL TECHNIQUES TO COMMUNICATE THE RESULTS OF THE STUDY.
- S.2.A Compare and contrast the benefits of different sampling techniques, including random sampling and convenience sampling methods.
- S.2.B Distinguish among observational studies, surveys, and experiments.
- S.2.C Analyze generalizations made from observational studies, surveys, and experiments.
- S.2.D Distinguish between sample statistics and population parameters.
- S.2.E Formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions.
- S.2.F Communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation.
- S.2.G Critically analyze published findings for appropriateness of study design implemented, sampling methods used, or the statistics applied.
VARIABILITY. THE STUDENT APPLIES THE MATHEMATICAL PROCESS STANDARDS WHEN DESCRIBING AND MODELING VARIABILITY.
- S.3.A Distinguish between mathematical models and statistical models.
- S.3.B Construct a statistical model to describe variability around the structure of a mathematical model for a given situation.
- S.3.C Distinguish among different sources of variability, including measurement, natural, induced, and sampling variability.
- S.3.D Describe and model variability using population and sampling distributions.
CATEGORICAL AND QUANTITATIVE DATA. THE STUDENT APPLIES THE MATHEMATICAL PROCESS STANDARDS TO REPRESENT AND ANALYZE BOTH CATEGORICAL AND QUANTITATIVE DATA.
- S.4.A Distinguish between categorical and quantitative data.
- S.4.B Represent and summarize data and justify the representation.
- S.4.C Analyze the distribution characteristics of quantitative data, including determining the possible existence and impact of outliers.
- S.4.D Compare and contrast different graphical or visual representations given the same data set.
- S.4.E Compare and contrast meaningful information derived from summary statistics given a data set.
- S.4.F Analyze categorical data, including determining marginal and conditional distributions, using two-way tables.
PROBABILITY AND RANDOM VARIABLES. THE STUDENT APPLIES THE MATHEMATICAL PROCESS STANDARDS TO CONNECT PROBABILITY AND STATISTICS.
- S.5.A Determine probabilities, including the use of a two-way table.
- S.5.B Describe the relationship between theoretical and empirical probabilities using the Law of Large Numbers.
- S.5.C Construct a distribution based on a technology-generated simulation or collected samples for a discrete random variable.
- S.5.D Compare statistical measures such as sample mean and standard deviation from a technology-simulated sampling distribution to the theoretical sampling distribution.
INFERENCE. THE STUDENT APPLIES THE MATHEMATICAL PROCESS STANDARDS TO MAKE INFERENCES AND JUSTIFY CONCLUSIONS FROM STATISTICAL STUDIES.
- S.6.A Explain how a sample statistic and a confidence level are used in the construction of a confidence interval.
- S.6.B Explain how changes in the sample size, confidence level, and standard deviation affect the margin of error of a confidence interval.
- S.6.C Calculate a confidence interval for the mean of a normally distributed population with a known standard deviation.
- S.6.D Calculate a confidence interval for a population proportion.
- S.6.E Interpret confidence intervals for a population parameter, including confidence intervals from media or statistical reports.
- S.6.F Explain how a sample statistic provides evidence against a claim about a population parameter when using a hypothesis test.
- S.6.G Construct null and alternative hypothesis statements about a population parameter.
- S.6.H Explain the meaning of the p-value in relation to the significance level in providing evidence to reject or fail to reject the null hypothesis in the context of the situation.
- S.6.I Interpret the results of a hypothesis test using technology-generated results such as large sample tests for proportion, mean, difference between two proportions, and difference between two independent means.
- S.6.J Describe the potential impact of Type I and Type II Errors.
BIVARIATE DATA. THE STUDENT APPLIES THE MATHEMATICAL PROCESS STANDARDS TO ANALYZE RELATIONSHIPS AMONG BIVARIATE QUANTITATIVE DATA.
- S.7.A Analyze scatterplots for patterns, linearity, outliers, and influential points.
- S.7.B Transform a linear parent function to determine a line of best fit.
- S.7.C Compare different linear models for the same set of data to determine best fit, including discussions about error.
- S.7.D Compare different methods for determining best fit, including median-median and absolute value.
- S.7.E Describe the relationship between influential points and lines of best fit using dynamic graphing technology.
- S.7.F Identify and interpret the reasonableness of attributes of lines of best fit within the context, including slope and y-intercept.