Construction Engineering 221

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Construction Engineering 221

• Probability and Statistics
• Location Measurement

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Location Measures

• Just like geographical location, statistical
  location uses a point of reference (mean, median,
  mode) and a distance (dispersion) from the
  reference point, or variance
• In normal distributions, the location measures
  reference the center of the distribution, or the
  most common measurement or observation

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Location Measures

• Midrange, mode, median, and mean are the standard
  measures of location
• Mode and midrange are seldom used, although mode
  can be helpful in some analyses (lots of zeroes,
  for example) to get an estimation of bias or
  validity
• Midrange is the halfway point
• Largest measure-smallest measure/2

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Location Measures

• Mode observation or measure occurring most
  frequently- no repeating measures, the sample has
  no mode, some observations repeated the same
  number of times, the sample is multimodal
• Median- middle observation the score or measure
  which has the same number of scores below as above

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Location Measures

• Mean- Xbar x1 x2 x3xi/n
• n number of observations or sample size
• Mean is good for comparing different samples
  (drug testing) and for powerful statistical tests
• Median is better measure of center when there are
  outliers or when the data is presented in
  classifications (cant use mean)

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Location Measures

• Median is the n/2 observation of rank ordered
  data. Can also be a classification (median grade
  was a C)
• Summation notation uses Sigma (S), with index of
  summation i and limit of summation n over a
  function or expression (ƒ)

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Location Measures

• Examples
• Si, i1,n10 means 12345678910
• S ƒ I1, n10 means 1 2 3 10
• Mean (Xbar) is S xi, i1, nn

n
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Location Measures

• In classifications, can take the mark times the
  frequency, and sum the multiples
• When added to measures of variance (dispersion),
  measures of location can be used to numerically
  describe a distribution of data and also to test
  some assumptions about the data, estimations of
  chance and probability, etc.