Hauptinhalt
Nebraska Math
High School: DATA
Students will solve problems and reason with data/probability using multiple representations, make connections within math and across disciplines, and communicate their ideas.
Formulate multi-variable statistical investigative questions and determine how data can be collected and analyzed to provide an answer.
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Apply an appropriate data collection plan when collecting primary data for the statistical investigative question of interest.
Use appropriate technology, including spreadsheet-based logic, to organize data for analysis.
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Distinguish between surveys, observational studies, and experiments.
Understand what constitutes good practice in designing a sample survey, an experiment, and an observational study.
Understand issues of bias and confounding variables in a study and their implications for interpretation.
Identify appropriate ways to summarize and then represent the distribution of univariate data and bivariate data through the construction of histograms, dot plots, stem plots, box plots, cumulative relative frequency graphs, time plots, circle graphs, stacked bar graphs, and mosaic bar graphs by hand or with technology.
Describe the shape, identify any outliers, and determine the spread of a data set.
Select and determine the appropriate measure of center based on the shape of a distribution and/or the presence of outliers.
Recognize when a data set can be reasonably said to be normally distributed and draw conclusions about the data from the associated normal distribution.
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data and recognize possible associations and trends in the data.
Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
Use technology to develop regression models for linear and non-linear data to predict unobserved outcomes. Interpret slope and y-intercept in the context of the problem.
Measure the strength of association using correlation coefficients for regression curves and interpret their meanings for the model.
Use residuals and residual plots to judge the quality of a regression model.
Recognize and explain when arguments based on data confuse correlation with causation.
Understand what constitutes statistical significance. Interpret statistical significance in the context of a situation and answer investigative questions appropriately.
Use probability as a tool for assessing risk and for informed decision making by interpreting P-values.
Describe events as subsets of a sample space using characteristics of the outcomes or as unions, intersections, or complements of other events.
Explain independent versus dependent probability of an event.
- Compound probability of independent events
- Conditional probability and independence
- Conditional probability and independence
- Dependent probability introduction
- General multiplication rule example: dependent events
- General multiplication rule example: independent events
- Independent events example: test taking
Determine when order in counting matters and use permutations and combinations to compute probabilities of events accordingly.
- Combination example: 9 card hands
- Combination formula
- Combinations
- Example: Different ways to pick officers
- Example: Lottery probability
- Factorial and counting seat arrangements
- Handshaking combinations
- Intro to combinations
- Mega millions jackpot probability
- Permutation formula
- Permutations
- Possible three letter words
- Probability using combinations
- Probability with combinations example: choosing cards
- Probability with combinations example: choosing groups
- Probability with permutations & combinations example: taste testing
- Probability with permutations and combinations
- Ways to arrange colors
- Ways to pick officers
Determine whether or not events are mutually exclusive (disjoint) and calculate their probabilities in either case.
Recognize and explain the concepts of conditional probability in everyday language and everyday situations.
- Conditional probability and independence
- Conditional probability and independence
- Conditional probability tree diagram example
- Conditional probability with Bayes' Theorem
- Dependent probability introduction
- General multiplication rule example: dependent events
- General multiplication rule example: independent events
- Independent events example: test taking
- Interpret probabilities of compound events
- Interpreting general multiplication rule
- Tree diagrams and conditional probability