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Construction Engineering 221

Construction Engineering 221. Probability and Statistics Location Measurement. 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

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Construction Engineering 221

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  1. Construction Engineering 221 Probability and Statistics Location Measurement

  2. 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

  3. 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

  4. 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

  5. Location Measures • Mean- Xbar + x1 + x2 + x3…xi/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 (can’t use mean)

  6. 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 (Σ), with index of summation i and limit of summation n over a function or expression (ƒ)

  7. Location Measures • Examples: • Σi, i=1,n=10 means 1+2+3+4+5+6+7+8+9+10 • Σ ƒ I=1, n=10 means 1 + 2 + 3 …+ 10 • Mean (Xbar) is Σ xi, i=1, n=n n

  8. 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.

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