S. Statistics and Probability
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S-ID.A. Summarize, represent, and interpret data on a single count or measurement variable
S-ID.A.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
S-ID.A.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
S-ID.A.3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
S-ID.A.4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
S-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables
S-ID.B.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
S-ID.B.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S-ID.B.6.a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
S-ID.B.6.b. Informally assess the fit of a function by plotting and analyzing residuals.
S-ID.B.6.c. Fit a linear function for a scatter plot that suggests a linear association.
S-ID.C. Interpret linear models
S-ID.C.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
S-ID.C.8. Compute (using technology) and interpret the correlation coefficient of a linear fit.
S-ID.C.9. Distinguish between correlation and causation.
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S-IC.A. Understand and evaluate random processes underlying statistical experiments
S-IC.A.1. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
S-IC.A.2. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability $0.5$. Would a result of $5$ tails in a row cause you to question the model?
S-IC.B. Make inferences and justify conclusions from sample surveys, experiments, and observational studies
S-IC.B.3. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
S-IC.B.4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
S-IC.B.5. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
S-IC.B.6. Evaluate reports based on data.
S-CP.A. Understand independence and conditional probability and use them to interpret data
S-CP.A.1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
S-CP.A.2. Understand that two events $A$ and $B$ are independent if the probability of $A$ and $B$ occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S-CP.A.3. Understand the conditional probability of $A$ given $B$ as \(P(\mbox{$A$ and $B$})/P(B)\), and interpret independence of $A$ and $B$ as saying that the conditional probability of $A$ given $B$ is the same as the probability of $A$, and the conditional probability of $B$ given $A$ is the same as the probability of $B$.
S-CP.A.4. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
S-CP.A.5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
S-CP.B. Use the rules of probability to compute probabilities of compound events in a uniform probability model
S-CP.B.6. Find the conditional probability of $A$ given $B$ as the fraction of $B$'s outcomes that also belong to $A$, and interpret the answer in terms of the model.
S-CP.B.7. Apply the Addition Rule, \(P(\mbox{$A$ or $B$}) = P(A) + P(B) - P(\mbox{$A$ and $B$})\), and interpret the answer in terms of the model.
S-CP.B.8. Apply the general Multiplication Rule in a uniform probability model, \(P(\mbox{$A$ and $B$}) = P(A)P(B|A) = P(B)P(A|B)\), and interpret the answer in terms of the model.
S-CP.B.9. Use permutations and combinations to compute probabilities of compound events and solve problems.
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- No tasks yet illustrate this standard.