Stat Unit 3--Winter 2008 - Central Tendency Where's the...

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Central Tendency Where’s the middle, what’s typical in a distribution? Mode Most frequently occurring category » Nominal data Median Value of the middle case when distribution is ranked » Ordinal data Mean Arithmetic average » Sum of case values divided by number of cases » Interval/ratio data
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Variability Once we know something about the center of a distribution, next question is To what degree do cases tend to be different or vary from this measure of the center
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Number of Children 0 5 10 15 20 25 30 0 4 8 12 16 20 24 28 32 36 40 44 49 53 57 61 65 Age Here’s a graph of the variability in age of students in a first grade class Variability is very small
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Here’s a graph of EMU students by age More variability than first grader example Number of Students 0 500 1000 1500 2000 2500 3000 3500 4000 0 4 8 12 16 20 24 28 32 36 40 44 49 53 57 61 65 AGE
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Number of People 0 200 400 600 800 1000 1200 0 4 8 12 16 20 24 28 32 36 40 44 49 53 57 61 65+ Age Finally, here’s a graph of population of Ypsilanti by age There is considerably more variability here
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Measures of variability depend on the level of measurement of the variable or attribute Nominal data Index of Qualitative Variation (IQV) is available » Rarely used Ordinal data Range and interquartile range Interval/ratio data Standard deviation
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