Describing Data Graphically

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Describing Data Graphically

• Module 2

2
Distribution of a Variable

• The distribution of a variable tells us the
  possible values for the variable and the
  probability that the variable takes these values.
• It is usually recommended that one looks at a
  graphical representation of the data before
  looking at the numerical descriptions (numerical
  data descriptions are found in module 3).

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Distribution of a Variable

• To describe a distribution we need 3 items

Graphics give a general idea of the shape,
center, and spread of the data.
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Describing Categorical Variable Distributions

• Suppose we poll 46 people on an issue. How can
  we exhibit their response?

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Describing Categorical Variable Distributions

• Suppose we poll 46 people on an issue. How can
  we exhibit their response?

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Describing Numeric Variable Distributions

• Example 1.5 on page 11 of the book shows how much
  50 consecutive shoppers spent in a store. The
  data appear as follows

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Describing Numeric Variable Distributions

• How can we describe the distribution of these 50
  numbers?

(not to be confused with a bar chart)
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Describing Numeric Variable Distributions

• How can we describe the distribution of these 50
  numbers?

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Describing Numeric Variable Distributions

• How can we describe the distribution of these 50
  numbers?

A Normal Quantile Plot compares the distribution
of the sample to the Normal Distribution)
Normal Quantile Plot
General Rule If the points of the plot generally
follow the diagonal line, the distribution is
roughly Normal.
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Describing Numeric Variable Distributions
Here is a histogram of some data I created that
follow a normal distribution pretty closely
This is the corresponding Normal Quantile Plot
for this data
Notice that the points of the plot follow the
diagonal line closely. This indicates that the
distribution is roughly normally distributed.
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Describing Numeric Variable Distributions
This is the histogram of the 50 numbers we have
been describing
It does not appear to follow the Normal
distribution (overlaid).
We examine the Normal Quantile Plot for this data
Notice the points do not very closely follow the
diagonal line, indicating the distribution is not
roughly Normal.
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Describing Numeric Variable Distributions
Histogram
Normal Quantile Plot
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Describing Numeric Variable Distributions

• Now, we examine the appearance of other data

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Describing Numeric Variable Distributions
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Describing Numeric Variable Distributions
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Describing Numeric Variable Distributions
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Describing Numeric Variable Distributions

• What are some possible explanations for outliers?
• The data point was recorded wrong.
• The data point wasnt actually a member of the
  population we were trying to sample.
• We just happened to get an extreme value in our
  sample.

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Describing Numeric Variable Distributions

• Symmetry versus Skewness

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Describing Numeric Variable Distributions

• Symmetry versus Skewness

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Describing Numeric Variable Distributions

• Symmetry versus Skewness