UCR SOC 005 STAT SPR 2010 Session 6 V1

# UCR SOC 005 STAT SPR 2010 Session 6 V1 - THE UNIVERSITY OF...

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Unformatted text preview: THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Session 6 Friday, 9 April 2009 David Swanson Watkins 1223 [email protected] SOCIOLOGY 005 STATISTICAL ANALYSIS THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Today’s Schedule Turn in Assignment 1 Lecture & Discussion: ‘Centrality’ and its measurement, Part 1 THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Central Tendency An estimate of the “center” of a distribution Three different types of estimates: Mean (Arithmetic, Harmonic , Geometric) Median Mode THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Recall the Notation X = a ‘variable’ X i = the value of ‘case ‘i’, where i = 1 to n (or N) X 1 , X 2 , X 3 , …,X n n = sample size N = population size Σ = summation sign Σ X i = the sum of the values for variable x from 1 to n (or N) THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Central Tendency Some Notation specific to central tendency The symbol μ (Greek: mu) is used to denote the arithmetic mean of an entire population. 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, x i , from that collection, μ = E{x i } is the expected value of that sample. µ = the mean of a given variable for a population THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Central Tendency Some Notation specific to central tendency If we denote a set of data by X = (x 1 , x 2 , ..., x n ), then the sample mean is typically denoted by m or by a horizontal bar over the variable ( enunciated " x bar"): THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of Mississippi Institute for Advanced Education in Geospatial Science Arithmetic Mean The most commonly used method of describing central tendency....
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UCR SOC 005 STAT SPR 2010 Session 6 V1 - THE UNIVERSITY OF...

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