Evidence of Understanding

**predict the theoretical probability of an event occurring based on a sample**- construct two way frequency tables and summarize data for each category
- identify
**joint,****marginal**and**conditional relative frequencies** - interpret relative frequencies in context and describe possible trends

- identify
- use the mean and
**standard deviation**of a data set to fit it to a normal distribution- use technology to calculate the mean and standard deviation of a data set
- analyze the variables, chart, or table of a data set and explain whether or not it is normally distributed

- describe the differences between a theoretical statistical distribution and the experimental distribution.
- determine, using a simulation, if a given set of experimental results are consistent with the theoretical results.

- construct two way frequency tables and summarize data for each category
**compare two data sets resulting from variation in the same set of parameters to determine if change in those parameters is statistically significant.***For example: Compare data sets from different groups in an experiment to see if the resulting data is statistically different.*- construct two way frequency tables and summarize data for each category
- identify
**joint,****marginal**and**conditional relative frequencies** - interpret relative frequencies in context and describe possible trends

- identify
- use simulations and experiments to generate two or more data sets
- recognize the similarities and differences between two data sets by examining different representations of the two data sets
- based on examining a simulation, determine the probability that the variation between two data sets is statistically significant (
__see this example__)

- construct two way frequency tables and summarize data for each category
**communicate statistical information in a variety of different formats and representations**- describe how different representations (graphs, charts, tables, formulas) can be used to communicate and potentially miscommunicate different meaning about statistics
- choose representations for communicating statistics based on the appropriateness of these representations

Develop conceptual understanding:

frequency, joint, marginal, conditional, relative, standard deviation, theoretical, empirical, experimental, statistically significantSupporting terms to communicate:

statistics, univariate, bivariate, measures of center, outlier, density, variability, standard deviation, distribution, spread, correlation, causation, interpolate, extrapolate, independent, dependent, domain, range, random, sample, categorized, summarized, discrete, continuous