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Lecture #4: Mean, Median, Mode.doc

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McMaster University
Jeff Racine

Lecture #4 (Chap 1 & 2 Continued) -With categorical data, you’re either in a category or not (unlike numerical where you have a chance of being in a category). Summary Statistics: Symbolic Expression • Population Parameters (typically unknown) I.e.: what is the true height of everyone living on earth right now -Summary statistics based on population data -Designated by Greek letters (eg: sigma, mew) • Sample Statistics (computed from sample) -Summary statistics based on sample data -Designated by Roman letters (eg: X bar, s) • Observed values -Traditionally represented by x or X -Different values indicated by subscripts 1,2,3 etc… (eg: X , X ,1X ,2…)3 • Observation Totals -Population total = N -Sample Total= n • In statistics, we often need to “accumulate” or “sum” some variable of interest • For example, A might denote, income, with A being the income of the first 1 person in our sample, A tha2 for the second and so on. • It Is supremely convenient to avoid having to write things like A 1 A +2A + 3 +A4+A +A +A 6 7 8 (A 1B) + (A 2B) + (A -3) + (A -4) 2 2 (A 1B) + (A -2) • One convenient operator that we shall use heavily is the “summation” (sigma) operator • The sum of a variable X can be written as Note: are often interchanged • Care must be taken when expanding sums. For instance, But note that, • Some useful manipulations involving the summation operator follow from the definition of the arithmetic function. • Common ones you may find useful are: Summary Measure Types • Central Tendency Measures -Locate a data set’
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