Chapter 4: Displaying Quantitative Data

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Chapter 4Displaying Quantitative Data
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A Distribution

• Bins
• Break up the span of values into equal-width
  piles.
• Counts
• The number of values that fall into each bin.
• Distribution of a quantitative variable
• The bins and counts
• Relative Frequency Histogram
• Displays the percentage of cases in each bin
• Faithful to area principle

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Stem-and-Leaf Displays

• Show the distribution.
• Turn display on its side.
• Looks similar to a histogram.
• Easy to make by hand for data sets that arent
  too large.
• Stem-and-Leaf Displays
• Contain all the information found in a histogram.
• Satisfy the area principle.
• Preserve the individual data values.

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Dotplots

• Dotplots
• Simple display for small data sets.
• Places dots for each case in the data.
• Show basic facts about a distribution.

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Shape, Center, and Spread

• To describe a distribution, discuss
• Shape
• Modes
• Unimodal single peak
• Bimodal two peaks
• Multimodal three or more peaks
• Uniform
• Doesnt appear to have any mode.
• All bars are approximately the same height.

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Shape, Center, and Spread

• To describe a distribution, discuss
• Shape
• Symmetry
• A symmetric histogram can fold in the middle so
  that the two sides almost match.
• Unusual features
• Mention any outliers that stand away from the
  body of the distribution.
• Gaps warn that the data may not be homogeneous.
• Data may come from different sources.
• Data may contain more than one group.

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Shape, Center, and Spread

• To describe a distribution, discuss
• Center
• An easy description of a typical value.
• A concise summary of the whole batch of numbers.
• Spread
• Look to see whether all the values of a
  distribution are tightly clustered around the
  center or spread out.

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Histograms TI Tips

• Enron data from 1997

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Comparing Distributions

• Compare the shapes.
• Modes
• Symmetry
• Unusual features
• Outliers
• Gaps
• Compare the centers.
• Compare the spread of each distribution.
• Check the scale!!

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Order

• When data are collected in a specific order,
  check to see if they have a pattern when plotted
  in that order.
• Timeplot

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Re-Expressing Skewed Data

• Apply a simple function to make a skewed
  distribution more symmetric.
• Skewed right try square roots or logarithms
• Skewed left try squaring

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What Can Go Wrong??

• Dont make a histogram of a categorical variable.
• Choose a scale appropriate to the data.
• Changing the bin width changes how the histogram
  looks.

• Avoid inconsistent scales.
• Label clearly.
• Show scale for both axes.
• Label each axis with the quantitative variable,
  including units.