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.

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.

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.

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.

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.

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.