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Displaying Distributions with Graphs Section 1.1

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Title: 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
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