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Unformatted text preview: THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Session 7 Monday, 12 April 2010 David Swanson Watkins 1223 David.swanson@ucr.edu SOCIOLOGY 005 STATISTICAL ANALYSIS THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Todays Schedule Lecture& Discussion: Centrality and its measurement, Part 2 Description of Assignment #2 THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Recall the definition of the Arithmetic Mean Arithmetic Mean Population = (x 1 + x 2 + + x n )/N = ( x i )/N Sample m = (x 1 + x 2 + + x n )/n = ( x i )/n THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science A Random Variable and Expectation* If a set of data is denoted by X = (x1, x2, ..., xn), then the samples arithmetic mean can be denoted by m. The arithmetic mean of the entire population (from which the sample is drawn) can be denoted by symbol (Greek: mu) * Largely taken From Wikipedia: http://en.wikipedia.org/wiki/Arithmetic_mean, last accessed August 2008 THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science A Random Variable and Expectation Or, for a random number that has a defined mean, is the probabilistic mean or expected value of the random number. If the set X is a collection of random numbers with probabilistic mean of , then for any individual sample, xi, from that collection, = E{xi} is the expected value of that sample. In practice, the difference between and m is that is typically unobservable because one observes only a sample rather than the whole population, and if the sample is drawn randomly, then one may treat m, but not , as a random variable, attributing a probability distribution to it (the sampling distribution of the mean). THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science A Random Variable and Expectation In practice, the difference between and is that is typically unobservable because one observes only a sample rather than the whole population, and if the sample is drawn randomly, then one may treat , but not , as a random variable, attributing a probability distribution to it (the sampling distribution of the mean). THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of...
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This note was uploaded on 10/16/2010 for the course SOC 5 taught by Professor Burke during the Spring '08 term at UC Riverside.
 Spring '08
 BURKE
 Sociology

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