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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

 A  = Assessment items available