Standards - Mathematics

Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.

Determine which measure of center best represents a real-world data set.

Interpret the measures of center and variability in the context of a problem.

Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

Use graphical representations of real-world data to describe the context from which they were collected.

Examine a sample of a population to generalize information about the population.

Differentiate between a sample and a population.

Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

Determine whether conclusions and generalizations can be made about a population based on a sample.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.

Informally explain situations in which statistical bias may exist.

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Use a number from 0 to 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event.

Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.

Collect and use data to predict probabilities of events.

Compare probabilities from a model to observed frequencies, explaining possible sources of discrepancy.

Approximate the probability of an event using data generated by a simulation (experimental probability) and compare it to the theoretical probability.

Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency.

Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams, and determine the probability of an event by finding the fraction of outcomes in the sample space for which the compound event occurred.

Design and use a simulation to generate frequencies for compound events.

Represent events described in everyday language in terms of outcomes in the sample space which composed the event.

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, describing patterns in terms of positive, negative, or no association, linear and non-linear association, clustering, and outliers.

Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line.

Use a linear model of a real-world situation to solve problems and make predictions.

Describe the rate of change and y-intercept in the context of a problem using a linear model of a real-world situation.

Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects, using relative frequencies calculated for rows or columns to describe possible associations between the two variables.

Examine a sample of a population to generalize information about the population.

Differentiate between a sample and a population.

Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

Determine whether conclusions and generalizations can be made about a population based on a sample.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and make predictions or conclusions about the population.

Informally explain situations in which statistical bias may exist. [Grade 7, 10]

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. [Grade 7, 11]

Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context. [Grade 7, 12]