Academic standards list

High School: Statistics & Probability — Mathematics


Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

Interpreting Categorical and Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable
Represent data with plots on the real number line (dot plots, histograms, and box plots).
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points
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
Summarize, represent, and interpret data on two categorical and quantitative variables
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
     There are 3 components within this standard.
Interpret linear models
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Distinguish between correlation and causation.

Making Inferences and Justifying Conclusions

Understand and evaluate random processes underlying statistical experiments
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
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
Make inferences and justify conclusions from sample surveys, experiments and observational studies
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
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
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Evaluate reports based on data.

Conditional Probability and the Rules of Probability

Understand independence and conditional probability and use them to interpret data
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,
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
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
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare
Use the rules of probability to compute probabilities of compound events in a uniform probability model
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
Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms
(+) Use permutations and combinations to compute probabilities of compound events and solve problems.

Measurement & Data

Calculate expected values and use them to solve problems
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated;
(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the
Use probability to evaluate outcomes of decisions
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
     There are 2 components within this standard.
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a
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