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Chapter 2: Organizing and Summarizing Data

Section 2.1: Organizing Qualitative Data

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 1.1:
      • qualitative data
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. Section 2.3:
      • identify graphical mispresentations of data

Learning Goals

  1. declarative knowledge (definitions)
    1. raw data
    2. frequency distribution
    3. relative frequency
    4. bar graph
    5. Pareto chart
    6. side-by-side bar graph
    7. pie chart (never appropriate for qualitative data!)
  2. procedural knowledge
    1. how to construct a frequency distribution (i.e., table)
    2. how to draw bar graph using frequency
    3. calculate relative frequency
    4. how to construct a relative frequency distribution (i.e., table)
    5. how to draw bar graph using relative frequency
    6. how to draw side-by-side bar graph using frequency data
    7. NOTE: All graphs MUST include:
      • long, descriptive title
      • labels for each axis
      • linear scales on each axis
  3. conditional knowledge
    1. how to check your work in relative frequency distributions
    2. how to identify the difference between frequency and relative frequency distributions
    3. how to identify the difference between frequency and relative frequency bar graphs
    4. how to interpret frequency bar graphs
    5. how to interpret relative frequency bar graphs
    6. the advantages and disadvantages of frequency bar graphs vs. relative frequency bar graphs
    7. the advantages of Pareto Charts
    8. why pie charts are inappropriate graphs (see also Section 2.3)

Section 2.2: Organizing Quantitative Data: The Popular Displays

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 1.1:
      • continuous quantitative data
      • discrete quantitative data
    2. Section 2.1:
      • frequency distribution
      • relative frequency distribution
  2. procedural knowledge
    1. Section 2.1:
      • how to calculate relative frequency
  3. conditional knowledge
    1. Section 2.3:
      • identify graphical mispresentations of data

Learning Goals

  1. declarative knowledge (definitions)
    1. classes
    2. histogram
    3. lower class limit
    4. upper class limit
    5. class width
    6. open-ended distribution
    7. open-ended classes, i.e., [x0, x1), [x1, x2), [x2, x3), ...
    8. stem-n-leaf plot (a.k.a., stemplot)
    9. split stems
    10. dot plot
    11. uniform distribution
    12. bell-shaped (i.e., normal) distribution
    13. outlier
    14. skewed right
    15. skewed left
    16. shapes of a distribution (there are five different shapes for this course)
    17. time-series data
    18. time-series plot
  2. procedural knowledge
    1. how to construct a histogram using TI83/84: http://stats.jjw3.com/math1431/ti83hist.htm
    2. how to change starting value and class width of a histogram using TI83/84: http://stats.jjw3.com/math1431/ti83hist.htm
    3. how to construct a histogram by hand
    4. how to construct a realtive frequency histogram by hand
    5. how to interpret a histogram
    6. how to describe the distribution of data in a histogram (i.e., shape, peak(s); apparent outliers)
    7. how to construct a stemplot using TI83/84: http://stats.jjw3.com/math1431/ti83stem.htm
    8. how to construct a stemplot by hand
    9. how to construct a back-to-back stemplot using TI83/84: http://stats.jjw3.com/math1431/ti83stem.htm
    10. how to construct a stemplot with split stems by hand
    11. how to describe the distribution of data in a stemplot (i.e., shape; peak(s); apparent outliers)
    12. how to construct a time-series plot with TI83/84 using TI83/84: http://stats.jjw3.com/math1431/ti83scatter.htm
  3. conditional knowledge
    1. explain how can a histogram be manipulated
    2. how to identify classes and class widths in a histogram
    3. how to interpret the bars in a frequency histogram
    4. how to interpret the bars in a relative frequency histogram
    5. explain why classes in a histogram are open intervals [a,b)
    6. identify the stem and leaf from raw data
    7. explain the advantages and disadvantages of a stemplot
    8. how to interpret the numbers in a stemplot
    9. identify the advantages of back-to-back stemplots
    10. identify the advantages and disadvantages of relative frequency histograms vs. frequency histograms
    11. explain the difference between histograms and bar graphs
    12. identify and explain why a histogram or stemplot is symmetric, skewed left, or skewed right
    13. how to identify apparent outliers
    14. how to interpret a time-series plot

Section 2.3: Graphical Misrepresentations of Data

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. none
  2. procedural knowledge
    1. Section 2.1:
      • constructing bar graphs
    2. Section 2.2:
      • constructing histograms
  3. conditional knowledge
    1. none

Learning Goals

  1. declarative knowledge (definitions)
    1. characteristics of good statistical graphs
  2. procedural knowledge
    1. how to identify and use characteristics of good statistical graphs
    2. how to identify misleading statistical graphs
  3. conditional knowledge
    1. explain why a statistical graph is misleading
    2. explain why a pie chart is a bad statistical graph

Chapter 2: Required Formulas – Need to Know for Tests

  1. Relative Frequency: relative frequency