### Standard 10: Statistics

In grades 9-12, the mathematics curriculum should include the continued study of data analysis and statistics so that students can:
• Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations
• Benchmarks 9D (The Mathematical World: Uncertainty)
The way data are displayed can make a big difference in how they are interpreted.

Benchmarks 9D (The Mathematical World: Uncertainty)
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)
Compare data for two groups by representing their averages and spreads graphically

Benchmarks 12C (Habits of Mind: Manipulation and Observation)
Use computers for producing tables and graphs and or making spreadsheet calculations.

Benchmarks 12E (Habits of Mind: Critical-Response Skills)
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)
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
• Benchmarks 12B (Habits of Mind: Computation and Estimation)
Use computer spreadsheets, graphing, and database programs to assist in quantitative analysis.

• Understand and apply measures of central tendency, variability, and correlation
• Benchmarks 9D (The Mathematical World: Uncertainty)
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)
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)
Choose appropriate summary statistics to describe group differences, always indicating the spread of the data as well as the data’s central tendencies.

• Understand sampling and recognize its role in statistical claims
• Benchmarks 9D (The Mathematical World: Uncertainty)
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)
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.

• Design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes
• Benchmarks 9D (The Mathematical World: Uncertainty)