Displaying Distributions with Graphs Section 1.1

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Displaying Distributions with GraphsSection 1.1
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Displaying Quantitative Variables Dotplots and
Stemplots

• How to construct a dotplot
• Label your axis and title your graph. Draw a
  horizontal line and label it with the variable.
  Title you graph.
• Scale the axis based on the values of the
  variable.
• Mark a dot above the number on the horizontal
  axis corresponding to each data value.

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To describe the overall pattern of a distribution

• Give the center and the spread.
• See if the distribution has a simple shape that
  you can describe in a few words.

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An outlier in any graph of data is an individual
observation that falls outside the overall
pattern of the graph.
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How to construct a stemplot

• Separate each observation into a stem consisting
  of all but the rightmost digit and a leaf, the
  final digit.
• Write the stems vertically in increasing order
  from top to bottom, and draw a vertical line to
  the right of the stems. Go through the data,
  writing each leaf to the right of its stem and
  spacing the leaves equally.
• Write the stems again, and rearrange the leaves
  in increasing order out from the stem.
• Title your graph and add a key describing what
  the stems and leaves represent.

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Displaying Quantitative Variables Histograms

• How to make a histogram
• Divide the range of data into classes of equal
  width. Count the number of observations in each
  class.
• Label and scale your axes, and title your graph.
  
• Draw a bar that represents the count in each
  class. Do not leave space between bars unless the
  class is empty.
• Graphing Note Add break-in-scale symbol // on
  an axis that does not begin with zero.

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Making Calculator Histograms

• Enter data in your statistics list editor
• Press STAT and choose 1Edit
• Type the values into list L1.

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Making Calculator Histograms Continued.

• 2. Set up a histogram in the statistics plots
  menu.
• Press 2nd Y (STAT PLOT).
• Press ENTER to go into Plot1.
• Adjust your setting as shown.

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Making Calculator Histograms Continued.

• 3. Set the window to match
• the classs intervals chosen .
• Press WINDOW.
• Enter the values shown.

• 4. Graph the histogram.
• Press GRAPH

• 5. Save the data in a named list for later use.
• From home screen, type the command L1?PREZ and
  press ENTER. The data are now stored in a list
  called PREZ.

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Histogram Hints

• There is no one right choice of classes in a
  histogram. Too few give a skyscraper effect, too
  many give us breakfast (pancake).
• Five classes is a good minimum.
• Our eyes respond to the area of the bars in a
  histogram. Be sure to choose classes that are
  the same width .
• If you are using a computer or calculator, beware
  of letting the device choose the classes.

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Describing a Distribution

• Concentrate on the main features.
• Look for major peaks and clear outliers.
• Look for rough symmetry a distribution is
  symmetric if the right and left sides are
  approximately mirror images.
• Look for skewness a distribution is skewed
  either right of left if the histogram has one
  side contains the observations with larger values.

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Homework

• 1.6, 1.8 (stemplot), 1.10, 1.12