- Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations

*Benchmarks* 9D (The Mathematical World: Uncertainty)

Grades 9-12, page 230

The way data are displayed can make a big difference in how they are
interpreted.

*Benchmarks* 9D (The Mathematical World: Uncertainty)

Grades 9-12, page 230

Both percentages and actual numbers have to be taken into account in
comparing different groups; using either category by itself could be misleading.

*Benchmarks* 12B (Habits of Mind: Computation and Estimation)

Grades 9-12, page 291

Compare data for two groups by representing their averages and spreads
graphically

*Benchmarks* 12C (Habits of Mind: Manipulation and Observation)

Grades 9-12, page 294

Use computers for producing tables and graphs and or making spreadsheet
calculations.

*Benchmarks* 12E (Habits of Mind: Critical-Response Skills)

Grades 9-12, page 300

Check graphs to see that they do not misrepresent results by using
inappropriate scales or by failing to specify the axes clearly.

*Benchmarks* 12E (Habits of Mind: Critical-Response Skills)

Grades 9-12, page 300

Suggest alternative ways of explaining data and criticize arguments
in which data, explanations, or conclusions are represented as the only
ones work consideration, with no mention of other possibilities. Similarly
suggest alternative trade-offs in decisions and designs and criticize those
in which major trade-offs are not acknowledged.

- Use curve fitting to predict from data
- Understand and apply measures of central tendency, variability, and correlation
- Understand sampling and recognize its role in statistical claims
- Design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes
- Analyze the effects of data transformations on measures of central tendency and variability

*Benchmarks* 12B (Habits of Mind: Computation and Estimation)

Grades 9-12, page 291

Use computer spreadsheets, graphing, and database programs to assist
in quantitative analysis.

*Benchmarks* 9D (The Mathematical World: Uncertainty)

Grades 9-12, page 230

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.

*Benchmarks* 9D (The Mathematical World: Uncertainty)

Grades 9-12, page 230

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.

*Benchmarks* 12D (Habits of Mind: Communication Skills)

Grades 9-12, page 297

Choose appropriate summary statistics to describe group differences,
always indicating the spread of the data as well as the data’s central
tendencies.

*Benchmarks* 9D (The Mathematical World: Uncertainty)

Grades 9-12, page 230

When people estimate a statistic, they may also be able to say how
far off the estimate might be.

*Benchmarks* 9D (The Mathematical World: Uncertainty)

Grades 9-12, page 230

The larger a well-chosen sample of a population is, the better 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.

*Benchmarks* 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.

*and so that, in addition, college-intending students can:*