Kathleen Z. Rooney
Common Core Standards for Mathematics (relevant standards included)
Summarize, represent, and interpret data on a single count or measurement variable
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1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
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2. Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
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3. Interpret differences in shape, center and spread in the context of the data sets.
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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.
Summarize, represent, and interpret data on two categorical and quantitative variables
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.
6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
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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.
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c. Fit a linear function for a scatter plot that suggests a linear association.
Interpret linear models
7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
9. Distinguish between correlation and causation.
Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying statistical experiments
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1. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
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2. Make inferences and justify conclusions from sample surveys, experiments, and observational studies
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3. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
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6. Evaluate reports based on data.
Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data
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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"").
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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.
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3. Understand the conditional probability of A given B as P(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.
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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.
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5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. Use the rules of probability to compute probabilities of compound events in a uniform probability model
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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.
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7. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B)
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8. Apply the general Multiplication Rule in a uniform probability model
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9. Use permutations and combinations to compute probabilities of compound events and solve problems.
Using Probability to Make Decisions
Calculate expected values and use them to solve problems
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1. Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space
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2. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
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4. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
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6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
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7. (+) Analyze decisions and strategies using probability concepts