Statistics and Probability

Understand that statistics can be used to gain information about a population by: • Recognizing that generalizations about a population from a sample are valid only if the sample is representative of that population. • Using random sampling to produce representative samples to support valid inferences.

Generate multiple random samples (or simulated samples) of the same size to gauge the variation in estimates or predictions, and use this data to draw inferences about a population with an unknown characteristic of interest.

Recognize the role of variability when comparing two populations.

Calculate the measure of variability of a data set and understand that it describes how the values of the data set vary with a single number. o Understand the mean absolute deviation of a data set is a measure of variability that describes the average distance that points within a data set are from the mean of the data set. o Understand that the range describes the spread of the entire data set. o Understand that the interquartile range describes the spread of the middle 50% of the data.

Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets.

Use measures of center and measures of variability for numerical data from random samples to draw comparative inferences about two populations.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency.

Develop a probability model and use it to find probabilities of simple events.

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Develop a probability model (which may not be uniform) by repeatedly performing a chance process and observing frequencies in the data generated.

Compare theoretical and experimental probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Determine probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

For an event described in everyday language, identify the outcomes in the sample space which compose the event, when the sample space is represented using organized lists, tables, and tree diagrams.

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