Statistics and Probability

Recognize that a statistical question is one that anticipates variability in the data related to the question and accounts for it in the answers.
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
Understand that the method and sample size used to collect data for a particular questions is intended to reduce the difference between a population and a sample taken from the population so valid inferences can be drawn about the population. Generate multiple samples (or simulated samples) of the same size to recognize the variation in estimates or predictions.
Understand that a set of quantitative data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Recognize that a measure of center for a quantitative data set summarizes all of its values with a single number while a measure of variation describes how its values vary with a single number.

Display quantitative data in plots on a number line, including dot plots, and histograms.
Summarize quantitative data sets in relation to their context.
- Report the number of observations.
- Describe the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Calculate range and measures of center, as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- Relate the range and the choice of measure of center to the shape of the data distribution and the context in which the data were gathered.

Understand that the probability of a chance event is a number between 0 and 1 inclusive, that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Approximate the probability of a simple event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
Develop a probability model and use it to find probabilities of simple events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
- Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of simple events.
- Develop a probability model (which may not be uniform) by observing frequencies in data generated from a change process.