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)
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

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.
 

• Understand and apply measures of central tendency, variability, and correlation

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.
 

• Understand sampling and recognize its role in statistical claims

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.
 

• Design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes

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.
 

• Analyze the effects of data transformations on measures of central tendency and variability

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

Transform data to aid in data interpretation and prediction

Test hypotheses using appropriate statistics