Standard 11: Statistics and Probability

In grades K-4, the curriculum should include experiences with data analysis and probability so that students can:

• Collect, organize, and describe data

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades 6-8, page 229
The larger a well-chosen sample is, the more accurately it is likely to represent the whole. But there are many ways of choosing a sample that can make it unrepresentative of the whole.

• Construct, read, and interpret displays of data

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 3-5, page 296
Use numerical data in describing and comparing objects and events.

Benchmarks 9A (The Mathematical World: Numbers)
Grades K-2, page 211
Simple graphs can help to tell about observations.

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades 3-5, page 228
Spreading data out on a number line helps to see what the extremes are, where they pile up, and where the gaps are. A summary of data includes where the middle is and how much spread is around it.

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades 3-5, page 228
A small part of something may be special in some way and not give and accurate picture of the whole. How much a portion of something can help to estimate what the whole is like depends on how the portion is chosen. There is a danger of choosing only the data that show what is expected by the person doing the choosing.

Benchmarks 9C (The Mathematical World: Shapes)
Grades 3-5, page 223
Graphical display of numbers may make it possible to spot patterns that are not otherwise obvious, such as comparative size or trends.
 

• Formulate and solve problems that involve collecting and analyzing data

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades K-2, page 227
Often a person can find out about a group of things by studying just a few of them.

Benchmarks 9D page 227 (The Mathematical World: Uncertainty)
Grades 3-5
Some predictions can be based on what is known about the past, assuming that conditions are pretty much the same now.

• Explore concepts of chance

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades K-2, page 222
Some things are more likely to happen than others. Some events can be predicted well and some cannot. Sometimes people aren’t sure what will happen because they don’t know everything that might be having an effect.

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades 3-5, page 227
Statistical predictions (as for rainy days, accidents) are typically better for what proportion of a group will experience something than for which members of the group will experience it and better for how often something will happen than for exactly when.

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades 3-5, page 228
Summary predictions are usually more accurate for large collections of events than for just a few. Even very unlikely events may occur fairly often in very large populations.