Topic: Reasoning and predicting from data |
Mathematics |
| Standard 6. Understands and applies basic and advanced concepts of statistics and data analysis |
| | Level III (Grade 6-8) |
| | | Benchmark 4. | Reads and interprets data in charts, tables, and plots (e.g., stem-and-leaf, box-and-whiskers, scatter) |
| | | | Knowledge/skill statements |
| | | | | 1. | Reads scatter plots |
| | | | | 2. | Interprets box-and-whisker plots |
| | | | | 3. | Reads box-and-whisker plots |
| | | | | 4. | Interprets stem-and-leaf plots |
| | | | | 5. | Reads stem-and-leaf plots |
| | | | | 6. | Interprets data in tables |
| | | Benchmark 5. | Uses data and statistical measures for a variety of purposes (e.g., formulating hypotheses, making predictions, testing conjectures) |
| | | | Knowledge/skill statements |
| | | | | 1. | Test conjectures using data |
| | | | | 2. | Makes predictions using data |
| | | | | 3. | Formulates hypotheses using data |
| | Level IV (Grade 9-12) |
| | | Benchmark 3. | Understands the concept of correlation (e.g., the difference between a "true" correlation and a "believable" correlation; when two variables are correlated) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the relationship between causality and correlation |
| | | | | 2. | Understands the concept of spurious correlation |
| | | | | 3. | Understands the concept of correlation |
| | | Benchmark 6. | Understands how the readerâ€™s bias, measurement error, and display distortion can affect the interpretation of data |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands how reader bias can affect data interpretation |
| | | | | 2. | Understands how measurement errors can affect data interpretation |
| | | | | 3. | Understands how display errors can affect data interpretation |
| | | Benchmark 9. | Understands that making an inference about a population from a sample always involves uncertainty and the role of statistics is to estimate the size of that uncertainty |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of statistical inference |
| | Level V (Grade (College Readiness)) |
| | | Benchmark 3. | Identifies patterns in graphical displays of data |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands graphical displays of data |
| | | | | 2. | Identifies trends in graphical displays of data |
| Standard 7. Understands and applies basic and advanced concepts of probability |
| | Level I (Grade K-2) |
| | | Benchmark 2. | Understands that some events can be predicted fairly well but others cannot because we do not always know everything that may affect an event |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that the more that is known about something the better the prediction |
| | | | | 2. | Understands that some things can be predicted better than others |
| | Level II (Grade 3-5) |
| | | Benchmark 3. | Understands that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that predictions assume that things will stay the same |
| | | | | 2. | Understands that predictions apply to the frequency of occurrence better than to specific events |
| | | Benchmark 4. | Understands that statistical predictions are better for describing what proportion of a group will experience something (e.g., what proportion of automobiles will be involved in accidents) rather than which individuals within the group will experience something, and how often events will occur (e.g., how many sunny days will occur over a year) rather than exactly when they will occur |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that predictions apply to proportions of groups better than individuals |
| | | | | 2. | Understands that predictions apply to how often events will occur better than when events will occur |
| | | Benchmark 5. | Uses basic sample spaces (i.e., the set of all possible outcomes) to describe and predict events |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of sample space |
| | | | | 2. | Uses basic sample spaces (set of all outcomes) to describe events |
| | | | | 3. | Uses basic sample spaces (set of all outcomes) to predict events |
| | Level III (Grade 6-8) |
| | | Benchmark 3. | Understands how predictions are based on data and probabilities (e.g., the difference between predictions based on theoretical probability and experimental probability) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands predictions based on experimental probability |
| | | | | 2. | Understands predictions based on theoretical probability |
| | | | | 3. | Contrasts predictions based on theoretical vs experimental probability |
| | | Benchmark 4. | Understands that the measure of certainty in a given situation depends on a number of factors (e.g., amount of data collected, what is known about the situation, how current data are) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that the certainty of conclusion(s) depend upon many factors |
| | | | | 2. | Understands that the certainty of conclusion(s) depends upon the currency of data |
| | | | | 3. | Understands that the certainty of conclusion(s) depend upon what is known about a situation |
| | | | | 4. | Understands that the certainty of conclusion(s) depend upon the amount of data |
| | Level IV (Grade 9-12) |
| | | Benchmark 5. | Understands the properties of the normal curve (i.e., the graph used to approximate the distribution of data for many real-world phenomena) and how the normal curve can be used to answer questions about sets of data |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands how the normal curve can be used to answers questions about data |
| | | | | 2. | Understands the properties of the normal curve |