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Math
Virginia Math
Algebra, Functions, and Data Analysis: Data Analysis
Formulate investigative questions that require the collection or acquisition of bivariate data, where exactly two of the variables are quantitative.
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Collect or acquire bivariate data from a representative sample to answer an investigative question.
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Represent bivariate data with a scatterplot using technology and describe how the variables are related in terms of the given context.
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Make predictions, decisions, and critical judgments using data, scatterplots, or the equation(s) of the mathematical model.
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Formulate questions that can be addressed with data and assess the type of data relevant to the question (e.g., quantitative versus categorical).
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Investigate, describe, and determine best sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling.
Plan and conduct an experiment and/or observational study. The experimental design should address control, randomization, and minimization of experimental error.
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Collect or acquire data to answer a statistical question.
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Recognize that data may contain errors, have missing values, or may be biased, and make decisions about how to account for these issues.
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Identify biased sampling methods.
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Given a plan for an observational study, identify possible sources of bias, and describe ways to reduce bias.
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Select, create, and use appropriate visual representations of data to brainstorm solutions.
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Use appropriate statistical methods to analyze data.
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Communicate the description of an experiment and/or observational study, the resulting data, analysis, and the validity of the conclusions.
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Analyze, interpret, and make predictions based on theoretical probability.
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Calculate conditional probabilities for dependent, independent, and mutually exclusive events.
- Calculating conditional probability
- Compound probability of independent events
- Conditional probability and independence
- Conditional probability and independence
- Conditional probability tree diagram example
- Conditional probability using two-way tables
- Dependent probability introduction
- Independent events example: test taking
- Tree diagrams and conditional probability
Represent and calculate probabilities using Venn diagrams, probability trees, organized lists, two-way tables, simulations, or other probability models.
- Addition rule for probability
- Addition rule for probability (basic)
- Calculating conditional probability
- Conditional probability and independence
- Conditional probability tree diagram example
- Conditional probability using two-way tables
- Interpret results of simulations
- Probability with Venn diagrams
- Tree diagrams and conditional probability
- Two-way tables, Venn diagrams, and probability
Interpret probabilities from simulations or experiments to make informed decisions and justify the rationale.
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Define and give contextual examples of complementary, dependent, independent, and mutually exclusive events.
- Addition rule for probability
- Addition rule for probability (basic)
- Compound probability of independent events
- Conditional probability and independence
- Conditional probability and independence
- Dependent probability introduction
- Independent events example: test taking
- Two-way tables, Venn diagrams, and probability
Given two or more events in a problem setting, determine whether the events are complementary, dependent, independent, and/or mutually exclusive.
- Addition rule for probability
- Addition rule for probability (basic)
- Compound probability of independent events
- Conditional probability and independence
- Conditional probability and independence
- Dependent probability introduction
- Independent events example: test taking
- Two-way tables, Venn diagrams, and probability
Compare and contrast permutations and combinations, including those in contextual situations.
Calculate the number of permutations of 𝑛 objects taken 𝑟 at a time, without repetition.
Calculate the number of combinations of 𝑛 objects taken 𝑟 at a time, without repetition.
Identify and describe the properties of a normal distribution.
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Determine when the normal distribution is a reasonable representation of the data.
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Describe how the mean and the standard deviation affect the graph of the normal distribution.
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Calculate and interpret the 𝑧-score for a data point, given the mean and the standard deviation.
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Compare two sets of normally distributed data using a standard normal distribution and 𝑧-scores, given the mean and the standard deviation.
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Represent probability as the area under the curve of a standard normal distribution.
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Determine probabilities associated with areas under the standard normal curve, using technology or a table of Standard Normal Probabilities.
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Investigate, represent, and determine relationships between a normally distributed data set and its descriptive statistics.
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