Chapter 3 Descriptive Statistics: Numerical Methods

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Chapter 3Descriptive StatisticsNumerical
Methods
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I. Measures of Location

• Quantitative data is described with measures of
  location and measures of dispersion. Measures of
  location are also called measures of central
  tendency. Examples include the mean, median, and
  mode.

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A. Mean

• Often referred to as the average, the mean is
  calculated as
• Sample mean
• Population mean

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B. Trimmed Mean

• Extremely high or low values will affect the mean
  and possibly lead to mistaken conclusions.

• The trimmed mean would drop the upper and lower
  5 of the data. This removes extreme values.

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C. Median

• This is the value in the middle of the data when
  the data are rank ordered from smallest to
  largest.
• Ex. 1,2,3,4,5. The median is 3.
• Ex. 2,4,6,8,10,12 The median is the mean of the
  middle two values (68)/27

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D. Mode

• The mode is the value in a sample that appears
  with the greatest frequency.
• Ex. 1,2,3,4,4,4,5 The mode is 4.
• Ex. 1,2,2,3,3,4 There are two modes, 2 and 3.
• Statisticians rarely report more than two modes.

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E. Percentiles

• The pth percentile is a value such that at least
  p of the items take this value or less and at
  least (100-p) of the items take this value or
  more.
• A good example of percentiles is how SAT scores
  are reported. When youre told you are in the
  90th percentile it means only 10 of the scores
  were above yours.

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How to calculate percentiles.

• 1. Rank order the data.
• 2. Compute an index i(p/100)n
• 3. a. If i isnt an integer, round up. The next
  integer greater than i is the position of the pth
  percentile.
• b. If i is an integer, the pth percentile is the
  average for the data values in positions i and
  (i1).