Statistics

Decisions or predictions are often based on data—numbers in context. These decisions or predictions would be easy if the data always sent a clear message, but the message is often obscured by variability in the data. Statistics provides tools for describing variability in data and for making informed decisions that take variability into account. Data are gathered, displayed, summarized, examined and interpreted to discover patterns. Data can be summarized by a statistic measuring center, such as mean or median, and a statistic measuring spread, such as interquartile range or standard deviation. Different distributions can be compared numerically using these statistics or visually using plots. Which statistics to compare, and what the results of a comparison might mean, depend on the question to be investigated and the real-life actions to be taken. Randomization has two important uses in drawing statistical conclusions. First, collecting data from a random sample of a population makes it possible to draw valid conclusions about the whole population, taking variability into account. Second, randomly assigning individuals to different treatments allows a fair comparison of the effectiveness of those treatments. A statistically significant outcome is one that is unlikely to be due to chance and this can be evaluated only under the condition of randomness. In critically reviewing uses of statistics in public media and other reports, it is important to consider the study design, how the data were collected, and the analyses employed as well as the data summaries and the conclusions drawn. //Connections to Probability, Functions and Modeling//. Valid conclusions about a population depend on designed simulations or other statistical studies using random sampling or assignment and rely on probability for their interpretation. Functional models may be used to approximate data. If the data are approximately linear, the relationship may be modeled with a trend line and the strength and direction of such a relationship may be expressed through a correlation coefficient. Technology facilitates the study of statistics by making it possible to simulate many possible outcomes in a short amount of time, and by generating plots, function models, trend lines and correlation coefficients.

Students understand that:
 * Core Concepts**
 * 1) Statistical methods take variability into account to support making informed decisions based on quantitative studies designed to answer specific questions.
 * 2) Visual displays and summary statistics condense the information in data sets into usable knowledge.
 * 3) Randomness is the foundation for using statistics to draw conclusions when testing a claim or estimating plausible values for a population characteristic.
 * 4) The design of an experiment or sample survey is of critical importance to analyzing the data and drawing conclusions.

Students can and do:
 * Core Skills**
 * 1) Formulate questions that can be addressed with data. Identify the relevant data, collect and organize it to respond to the question.
 * 2) Use appropriate displays and summary statistics for data.
 * 3) Interpret data displays and summaries critically; draw conclusions and develop recommendations.
 * 4) Draw statistical conclusions involving population means or proportions using sample data.
 * 5) Evaluate reports based on data.