Probability and Statistics (Virginia SOL)

Data in Context (DC)

• PS.DC.1 Use the statistical problem-solving cycle to pose questions and identify data types, sources and limits.
• Explain the stages of the statistical cycle and how they connect.
• Pose questions and form conclusions that fit the context.
• Decide whether the data needed are quantitative or categorical.
• Tell a population from a sample and a parameter from a statistic.
• Identify and explain the limits of a statistical approach.
• PS.DC.2 Compare ways of collecting data and plan and carry out an observational study.
• Describe simple random, stratified, systematic and cluster sampling.
• Choose the best sampling method for a situation.
• Explain sampling bias and kinds of response bias.
• Use the statistical cycle to plan an observational study.
• PS.DC.3 Apply the principles of experimental design to plan and run a well-designed experiment.
• Describe control groups, blinding and placebos, experimental units and blocking or matched pairs.
• Evaluate comparison, randomization, replication and control in a given study.
• Contrast controlled experiments with observational studies and what each can conclude.
• Use the statistical cycle to plan a well-designed experiment.
• Choose a data collection method that suits the context.

Descriptive Statistics (DS)

• PS.DS.1 Graph quantitative data for one variable and describe its pattern, center, spread and unusual features.
• Make and interpret dot plots, stemplots, boxplots, cumulative frequency graphs and histograms with technology.
• Analyze graphs for shape, center, spread and unusual features in context.
• PS.DS.2 Interpret the numerical summaries of a one-variable data set, including outliers.
• Interpret the mean, median and mode.
• Interpret the range, interquartile range, variance and standard deviation.
• Identify possible outliers with a rule.
• Explain how outliers affect a data set.
• Explain how the standard deviation formula measures spread.
• PS.DS.3 Compare two or more one-variable quantitative data sets numerically and graphically.
• Make back-to-back stemplots, parallel dot plots and boxplots, and histograms.
• Compare the data sets by shape, center, spread and unusual features.
• PS.DS.4 Represent and analyze categorical data with two-way tables and graphs.
• Make and interpret bar graphs for one categorical variable.
• Make and interpret segmented and side-by-side bar graphs to compare distributions.
• Make and interpret a two-way table.
• Calculate and interpret marginal, relative and conditional frequencies.
• PS.DS.5 Use scatterplots to describe the relationship between two quantitative variables.
• Make scatterplots with technology.
• Interpret form, direction, strength and unusual features in context.
• PS.DS.6 Build and interpret a least-squares regression model to describe how two variables are related.
• Make the model with technology and interpret its slope and y-intercept in context.
• Calculate and interpret the correlation coefficient r.
• Calculate and interpret the coefficient of determination r².
• Make predictions and recognize limits such as extrapolation.
• Calculate and interpret a residual.
• Calculate and interpret the standard deviation of the residuals, s.

Probability (P)

• PS.P.1 Organize information and use probability rules to find probabilities of events in context.
• Decide whether events are complementary, dependent, independent or mutually exclusive and find their probabilities.
• Show and calculate probabilities with Venn diagrams, tree diagrams and two-way tables.
• Apply the addition, multiplication and complement rules.
• Use conditional probabilities to judge association or independence.
• PS.P.2 Model and interpret situations with discrete random variables, including binomial distributions.
• Identify discrete random variables and build valid probability distribution tables.
• Calculate and interpret the mean and standard deviation of a discrete random variable.
• Decide whether a variable meets the conditions for a binomial setting.
• Design and carry out a binomial simulation.
• Calculate and interpret binomial probabilities in context.
• Calculate the mean and standard deviation of a binomial distribution.
• Describe the center, shape and spread of a discrete random variable in context.
• PS.P.3 Model and interpret situations with normal distributions.
• Compare discrete and continuous distributions.
• Show probability as area under a normal curve with the Empirical Rule and technology.
• Describe the center, shape and spread of normal distributions in context.
• Compare normal data sets with z-scores, percentiles or probabilities.
• Standardize a value from a normal distribution and interpret the z-score.
• Calculate and interpret normal probabilities with technology.

Inferential Statistics (IS)

• PS.IS.1 Use sampling distributions and inference to make decisions about population proportions.
• Describe the shape, center and spread of the sampling distribution of a sample proportion.
• Build a one-sample z confidence interval for a proportion: check conditions, compute with technology, interpret.
• Explain how confidence level and sample size affect interval width and margin of error.
• Calculate and interpret a point estimate and margin of error for a proportion.
• Explain how a hypothesis test supports a statistical decision.
• Carry out a one-sample z test for a proportion: hypotheses, conditions, p-value, decision and conclusion.
• Use the statistical cycle to plan and carry out a study of a proportion using inference.
• PS.IS.2 Use sampling distributions and inference to make decisions about population means.
• Describe the shape, center and spread of the sampling distribution of a sample mean.
• Calculate and interpret a point estimate and margin of error for a mean.
• Describe how the Central Limit Theorem supports inference about a mean.
• Identify the properties of a t distribution.
• Build a one-sample t confidence interval: check conditions, compute with technology, interpret.
• Carry out a one-sample t test: hypotheses, conditions, p-value, decision and conclusion.