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## Math 7-9

Math 7-9 > Factors > Statistical Reasoning

# Statistical Reasoning

## Factor Connections

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How Statistical Reasoning connects to...

Statistical Reasoning involves thinking about and understanding uncertainty and building mental models to capture key aspects of real world phenomena. As students reason with this uncertainty, they should be able to formulate questions about data and determine what data they need to answer these questions. They then gather, organize, analyze, and display this data to describe and make inferences to help them answer their questions.

### Main Ideas

Statistical Reasoning involves an integrated conceptual understanding of statistics and probability:

• Statistical thinking includes using critical thinking to organize, represent, analyze, and interpret data; understanding how to use the appropriate statistical tools; explaining statistical processes; connecting statistical concepts; and understanding experimental design.
• Probabilistic thinking includes calculating the likelihood of future events, including what kinds of distributions of chance events may be expected and how rare or common a particular outcome will be.

Key concepts involved in developing statistical and probabilistic thinking are:

• Center: The average value of the data, typically measured by the mean or median;
• Distribution: A collection of all the values in the set of data presented in an organized manner such as a table or graph (e.g., a bell curve representing the frequency of each value);
• Spread or Variability: How similar or different the set of values is from the center (e.g., range) in a distribution; and
• Randomness: The lack of a pattern in a set of events.

Competency in statistical and probabilistic thinking enables students to reason about and discuss what data means, including the ability to use models that quantify important aspects of data that can have uncertainty, noise, and error.

Both statistical and probabilistic thinking can be influenced by the context in which the data or events occur. Further, students' prior knowledge, beliefs, and any misconceptions about chance or uncertain situations may influence the quality of their Statistical Reasoning.