Benchmark 9D: The Mathematical World : Uncertainty
(grades 9-12, page 230)

• Even when there are plentiful data, it may not be obvious what mathematical model to use to make predictions from them or there may be insufficient computing power to use some models. (1 of 8)
• Standard 10-5 page 167, Grades 9-12
Design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes
• When people estimate a statistic, they may also be able to say how far off the estimate might be. (2 of 8)
• Standard 10-4 page 167, Grades 9-12
Understand sampling and recognize its role in statistical claims
• The middle of a data distribution may be misleading when the data are not distributed symmetrically, or when there are extreme high or low values, or when the distribution is not reasonably smooth. (3 of 8)
• Standard 10-3 page 167, Grades 9-12
Understand and apply measures of central tendency, variability, and correlation
• The way data are displayed can make a big difference in how they are interpreted. ( 4 of 8)
• Standard 10-1 page 167, Grades 9-12
Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations
• Both percentages and actual numbers have to be taken into account in comparing different groups; using either category by itself could be misleading. (5 of 8)
• Standard 10-1 page 167, Grades 9-12
Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations
• Considering whether two variables are correlated requires inspecting their distributions, such as in two-way tables or scatterplots. A believable correlation between two variables doesn't mean that either one causes the other; perhaps some other variable causes them both or the correlation might be attributable to chance alone. A true correlation means that differences in one variable imply differences in the other when all other things are equal. (6 of 8)
• Standard 10-3 page 167, Grades 9-12
Understand and apply measures of central tendency, variability, and correlation
• The larger a well-chosen sample of a population is, the better it estimates population summary statistics. For a well-chosen sample, the size of the sample is much more important than the size of the population. To avoid intentional or unintentional bias, samples are usually selected by some random system. (7 of 8)
• Standard 10-4 page 167, Grades 9-12
Understand sampling and recognize its role in statistical claims
• A physical or mathematical model can be used to estimate the probability of real-world events. (8 of 8)
• Standard 11-2 page 171, Grades 9-12
Use simulations to estimate probabilities