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UCR SOC 005 STAT SPR 2010 Session 7 V1

UCR SOC 005 STAT SPR 2010 Session 7 V1 -...

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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 [email protected] SOCIOLOGY 005 STATISTICAL ANALYSIS

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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Today’s 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     µ  = (x 1  + x 2  + … + x n )/N  = ( Σ x i )/N        Sample    m  = (x 1  + x 2  + … + x n )/n  = ( Σ x i )/n

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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  sample’s 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  μ  (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,  μ  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  μ , then for any individual sample, xi, from that  collection,  μ  = E{xi} is the expected value of that sample.  In practice, the difference between  μ  and m is that  μ  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  μ , as a random  variable, attributing a probability distribution to it (the sampling  distribution of the mean).

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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  μ  and  is that  μ  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  μ , 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

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