Topic: Data distribution |
Mathematics |
| Standard 6. Understands and applies basic and advanced concepts of statistics and data analysis |
| | Level II (Grade 3-5) |
| | | Benchmark 2. | Understands that spreading data out on a number line helps to see what the extremes are, where the data points pile up, and where the gaps are |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of gaps in data |
| | | | | 2. | Understands the concept of extremes in data |
| | | | | 3. | Understands the concept of clusters in data |
| | | | | 4. | Uses a number line to see gaps in data |
| | | | | 5. | Uses a number line to see extremes in data |
| | | | | 6. | Uses a number line to see clusters in data |
| | | Benchmark 3. | Understands that a summary of data should include where the middle is and how much spread there is around it |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of the middle of the data distribution |
| | | | | 2. | Understands the concept of the spread of data |
| | | | | 3. | Understands the concept of summarizing data |
| | Level III (Grade 6-8) |
| | | Benchmark 1. | Understands basic characteristics of measures of central tendency (i.e., mean, mode, median) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of central tendency |
| | | | | 2. | Understands the concept of the mean |
| | | | | 3. | Computes mean |
| | | | | 4. | Understands the concept of the mode |
| | | | | 5. | Computes mode |
| | | | | 6. | Understands the concept of the median |
| | | | | 7. | Computes median |
| | | Benchmark 2. | Understands basic characteristics of frequency and distribution (e.g., range, varying rates of change, gaps, clusters) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of gaps |
| | | | | 2. | Understands the concept of varying rates of change |
| | | | | 3. | Understands the concept of a frequency distribution |
| | | | | 4. | Understands the concept of clusters |
| | | | | 5. | Understands the concept of range |
| | | | | 6. | Computes range |
| | | Benchmark 3. | Understands the basic concepts of center and dispersion of data |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of dispersion |
| | | | | 2. | Understands the concept of data dispersion around the center |
| | | Benchmark 9. | Understands the basic concept of outliers |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of outliers |
| | Level IV (Grade 9-12) |
| | | Benchmark 2. | Understands measures of central tendency and variability (e.g., standard deviation, range, quartile deviation) and their applications to specific situations |
| | | | Knowledge/skill statements |
| | | | | 1. | Computes standard deviation |
| | | | | 2. | Understands the concept of range |
| | | | | 3. | Understands the concept of quartile deviation |
| | | | | 4. | Computes quartile deviation |
| | | | | 5. | Understands the concept of standard deviation |
| | | | | 6. | Understands the relationship between central tendency and dispersion |
| | | | | 7. | Computes range |
| | | | | 8. | Understands the concept of quartiles |
| | | | | 9. | Computes quartiles |
| | | 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 4. | Understands different methods of curve-fitting (e.g., median-fit line, regression line) and various applications (e.g., making predictions) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the median-fit method of curve fitting |
| | | | | 2. | Understands the least squares method of curve fitting |
| | | | | 3. | Understands prediction as it relates to curve fitting |
| | | | | 4. | Understands the concept of curve fitting |
| | | Benchmark 5. | 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 how outliers can affect a regression line |
| | | | | 2. | Understands how a scatter plot helps identify outliers |
| | | 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 |
| Standard 7. Understands and applies basic and advanced concepts of probability |
| | 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 |