Descriptive statistics

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Descriptive statistics

• Describing data with numbers
• measures of location

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What to describe?

• What is the location or center of the data?
• How do the data vary?

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Measures of Location

• Mean
• Median
• Mode

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Mean

• Denoted by x-bar ( )
• Seriously affected by unusual values
  (outliers).
• Appropriate for measurement data and
  equally-spaced ordinal data.

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Median

• Robust to outliers, that is, not affected much
  by unusual values.
• Appropriate for measurement data and ordinal data.

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Mode

• The value that occurs most frequently.
• One data set can have many modes.
• Appropriate for all types of data.

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The most appropriate measure of location depends
on
the shape of the datas distribution.
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Most appropriate measure of location

• Depends on whether or not data are symmetric or
  skewed.
• Depends on whether or not data have one
  (unimodal) or more (multimodal) modes.

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Symmetric and Unimodal
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Symmetric and Unimodal
Descriptive Statistics Variable N Mean
Median TrMean StDev SE Mean GPA 92
3.0698 3.1200 3.0766 0.4851 0.0506 Variable
Minimum Maximum Q1 Q3 GPA
2.0200 3.9800 2.6725 3.4675
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Symmetric and Bimodal
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Symmetric and Bimodal
13
Symmetric and Bimodal
Descriptive Statistics Variable N Mean
Median TrMean StDev SE Mean Height 64
68.614 69.000 68.634 3.802 0.475 Variable
Minimum Maximum Q1 Q3 Height 61.000
76.000 65.125 72.000
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Skewed Right
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Skewed Right
Descriptive Statistics Variable N Mean
Median TrMean StDev SE Mean q39 92
61.04 46.50 52.93 62.90 6.56 Variable
Minimum Maximum Q1 Q3 q39
0.00 400.00 21.50 83.00
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Choosing Appropriate Measure of Location

• If data are symmetric, the mean, median, and mode
  will be approximately the same.
• If data are multimodal, report the mean, median
  and/or mode for each subgroup.
• If data are skewed, report the median.