Topic: Data collection and sampling |
Mathematics |
| Standard 6. Understands and applies basic and advanced concepts of statistics and data analysis |
| | Level Pre-K (Grade Pre-K) |
| | | Benchmark 2. | Collects data from everyday (real-world) situations (e.g., favorite color, number of pets) |
| | | | Knowledge/skill statements |
| | | | | 1. | Collects data from everyday situations, such as favorite colors |
| | | | | 2. | Collects data from everyday situations, such as number of pets |
| | Level I (Grade K-2) |
| | | Benchmark 2. | Understands that one can find out about a group of things by studying just a few of them |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that a few members of a group can show what is common to the group |
| | Level II (Grade 3-5) |
| | | Benchmark 1. | Understands that data represent specific pieces of information about real-world objects or activities |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that data represents specific pieces of information about the real world |
| | | Benchmark 6. | Understands that data come in many different forms and that collecting, organizing, and displaying data can be done in many ways |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that data can be organized in many ways |
| | | | | 2. | Understands that data can be collected in many ways |
| | | | | 3. | Understands that data can be displayed in many ways |
| | | | | 4. | Understands that data comes in different forms |
| | | Benchmark 7. | Understands the basic concept of a sample (e.g., a large sample leads to more reliable information; a small part of something may have unique characteristics but not be an accurate representation of the whole) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that a small sample of something may be unique and not representative of the whole |
| | | | | 2. | Understands the basic concept of a sample |
| | | | | 3. | Understands that large sample sizes lead to more reliable information |
| | Level III (Grade 6-8) |
| | | Benchmark 10. | Understands basic concepts about how samples are chosen (e.g., random samples, bias in sampling procedures, limited samples, sampling error) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a random sample |
| | | | | 2. | Understands bias in sampling |
| | | | | 3. | Understands the concept of a limited sample |
| | | | | 4. | Understands the basic process of how samples are chosen |
| | | | | 5. | Understands the concept of a sampling error |
| | | | | 6. | Understands the concept of a sample |
| | Level IV (Grade 9-12) |
| | | Benchmark 7. | Understands sampling distributions, the central limit theorem, and confidence intervals |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of sampling distribution |
| | | | | 2. | Understands the concept of confidence intervals |
| | | | | 3. | Understands the concept of the central limit theorem |
| | | Benchmark 8. | Understands how concepts of representativeness, randomness, and bias in sampling can affect experimental outcomes and statistical interpretations |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of representativeness in sampling |
| | | | | 2. | Understands the concept of randomness in sampling |
| | | | | 3. | Understands the concept of bias in sampling |
| | | | | 4. | Understands how representativeness in sampling can affect experimental outcomes |
| | | | | 5. | Understands how representativeness in sampling can affect statistical interpretations |
| | | | | 6. | Understands how randomness in sampling can affect experimental outcomes |
| | | | | 7. | Understands how randomness in sampling can affect statistical interpretations |
| | | | | 8. | Understands how bias in sampling can affect experimental outcomes |
| | | | | 9. | Understands how bias in sampling can affect statistical interpretations |
| | | 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 1. | Knows how to design simple experiments to collect data and answer questions |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands a hypothesis statement |
| | | | | 2. | Understands methods of sampling |
Business Education |
| Standard 13. Analyzes and interprets data using common statistical procedures, charts, and graphs |
| | Level IV (Grade 9-12) |
| | | Benchmark 1. | Uses statistical concepts to analyze data, evaluate results, and draw conclusions (e.g., data found in financial reports) |
| | | | Knowledge/skill statements |
| | | | | 1. | Uses statistical concepts to analyze data |
| | | | | 2. | Uses statistical concepts to evaluate results |
| | | | | 3. | Uses statistical concepts to draw conclusions |
| | | | | 4. | Uses statistical concepts to analyze data found in financial reports |
| | | Benchmark 2. | Uses tables, graphs, diagrams, and charts to obtain or convey quantitative information (e.g., manual or electronic representations) |
| | | | Knowledge/skill statements |
| | | | | 1. | Uses tables to obtain quantitative information |
| | | | | 2. | Uses graphs to obtain quantitative information |
| | | | | 3. | Uses diagrams to obtain quantitative information |
| | | | | 4. | Uses charts to obtain quantitative information |
| | | | | 5. | Uses tables to convey quantitative information |
| | | | | 6. | Uses graphs to convey quantitative information |
| | | | | 7. | Uses diagrams to convey quantitative information |
| | | | | 8. | Uses charts to convey quantitative information |
| | | | | 9. | Uses manual representations to obtain quantitative information |
| | | | | 10. | Uses manual representations to convey quantitative information |
| | | | | 11. | Uses electronic representations to obtain quantitative information |
| | | | | 12. | Uses electronic representations to convey quantitative information |
| | | Benchmark 3. | Calculates measures of central tendency (i.e., mean, median, mode) and variability (e.g., standard deviation, range, quartile deviation) |
| | | | Knowledge/skill statements |
| | | | | 1. | Calculates measures of central tendency |
| | | | | 2. | Calculates measures of variability |
| | | | | 3. | Calculates measures of mean |
| | | | | 4. | Calculates measures of median |
| | | | | 5. | Calculates measures of mode |
| | | | | 6. | Calculates measures of standard deviation |
| | | | | 7. | Calculates measures of range |
| | | | | 8. | Calculates measures of quartile deviation |
| | | Benchmark 4. | Understands how outliers may affect various representations of data (e.g., a regression line might be strongly influenced by a few aberrant points, whereas the scatter plot for the same data might suggest that the aberrant points represent mistakes) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that a regression line might be strongly influenced by a few aberrant points |
| | | | | 2. | Understands that a scatter plot might suggest that aberrant points represent mistakes |
| | | Benchmark 5. | Understands how the readerâ€™s bias, measurement error, and display distortion can affect the interpretation of data |
| | | | Knowledge/skill statements |
| | | | | 2. | Understands how measurement error can affect the interpretation of data |
| | | Benchmark 6. | 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 that making an inference about a population from a sample always involves uncertainty |
| | | | | 2. | Understands that the role of statistics is to estimate the size of uncertainty about an inference made from a sample |