# List of Benchmarks for Mathematics |

**Standard 6.** | Understands and applies basic and advanced concepts of statistics and data analysis |

| ** Level Pre-K (Grade Pre-K)** |

| 1. | Knows that concrete and pictorial graphs represent information |

| 2. | Collects data from everyday (real-world) situations (e.g., favorite color, number of pets) |

| ** Level I (Grade K-2)** |

| 1. | Collects and represents information about objects or events in simple graphs |

| 2. | Understands that one can find out about a group of things by studying just a few of them |

| ** Level II (Grade 3-5)** |

| 1. | Understands that data represent specific pieces of information about real-world objects or activities |

| 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 |

| 3. | Understands that a summary of data should include where the middle is and how much spread there is around it |

| 4. | Organizes and displays data in simple bar graphs, pie charts, and line graphs A |

| 5. | Reads and interprets simple bar graphs, pie charts, and line graphs A |

| 6. | Understands that data come in many different forms and that collecting, organizing, and displaying data can be done in many ways |

| 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) |

| ** Level III (Grade 6-8)** |

| 1. | Understands basic characteristics of measures of central tendency (i.e., mean, mode, median) A |

| 2. | Understands basic characteristics of frequency and distribution (e.g., range, varying rates of change, gaps, clusters) |

| 3. | Understands the basic concepts of center and dispersion of data |

| 4. | Reads and interprets data in charts, tables, and plots (e.g., stem-and-leaf, box-and-whiskers, scatter) A |

| 5. | Uses data and statistical measures for a variety of purposes (e.g., formulating hypotheses, making predictions, testing conjectures) |

| 6. | Organizes and displays data using tables, graphs (e.g., line, circle, bar), frequency distributions, and plots (e.g., stem-and-leaf, box-and-whiskers, scatter) A |

| 7. | Understands faulty arguments, common errors, and misleading presentations of data |

| 8. | Understands that the same set of data can be represented using a variety of tables, graphs, and symbols and that different modes of representation often convey different messages (e.g., variation in scale can alter a visual message) |

| 9. | Understands the basic concept of outliers |

| 10. | Understands basic concepts about how samples are chosen (e.g., random samples, bias in sampling procedures, limited samples, sampling error) A |

| ** Level IV (Grade 9-12)** |

| 1. | Selects and uses the best method of representing and describing a set of data (e.g., scatter plot, line graph, two-way table) |

| 2. | Understands measures of central tendency and variability (e.g., standard deviation, range, quartile deviation) and their applications to specific situations |

| 3. | Understands the concept of correlation (e.g., the difference between a "true" correlation and a "believable" correlation; when two variables are correlated) |

| 4. | Understands different methods of curve-fitting (e.g., median-fit line, regression line) and various applications (e.g., making predictions) |

| 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) |

| 6. | Understands how the reader’s bias, measurement error, and display distortion can affect the interpretation of data |

| 7. | Understands sampling distributions, the central limit theorem, and confidence intervals |

| 8. | Understands how concepts of representativeness, randomness, and bias in sampling can affect experimental outcomes and statistical interpretations |

| 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 |

| ** Level V (Grade (College Readiness))** |

| 1. | Knows how to design simple experiments to collect data and answer questions |

| 2. | Evaluates reports in the media in terms of the sources of the data and the design of the study |

| 3. | Identifies patterns in graphical displays of data |

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A = Assessment items available |