**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