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CENTRAL TENDENCY: MEAN, MEDIAN, MODE

CENTRAL TENDENCY: MEAN, MEDIAN, MODE. ASSIGNMENTS. Pollock, Essentials , chs. 2-3 Begin exploring Pollock, SPSS Companion, introduction and chs. 1-2 Sections in Sol í s 105. Why Central Tendency?. Summation of a variable Possibilities of comparison: Across time

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CENTRAL TENDENCY: MEAN, MEDIAN, MODE

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  1. CENTRAL TENDENCY: MEAN, MEDIAN, MODE

  2. ASSIGNMENTS • Pollock, Essentials, chs. 2-3 • Begin exploring Pollock, SPSS Companion, introduction and chs. 1-2 • Sections in Solís 105

  3. Why Central Tendency? • Summation of a variable • Possibilities of comparison: • Across time • Across categories (e.g. countries, classes) • But beware of limitations!

  4. Outline: Measures ofCentral Tendency Mean or “average” value: • Definition • Illustration • Special properties (for future reference) Median or middle value: • Definition • Comparison with mean Mode or most frequent value: • Definition • Applications

  5. Computing the Arithmetic Mean

  6. Finding the Arithmetic Mean

  7. Properties of the Arithmetic Mean

  8. Illustration: Properties of the Arithmetic Mean • Data: 3, 4, 5, 6, 7 • Mean = 25/5 = 5 Differences from mean: Squared differences: 3 – 5 = -2 4 4 – 5 = -1 1 5 – 5 = 0 0 6 – 5 = +1 1 7 – 5 = +2 4 Sum (Σ) = 0 Sum (Σ) = 10

  9. Treating Other Numbers (e.g., 3) as Mean: Differences: Squared differences: 3 – 3 = 0 0 4 – 3 = +1 1 5 – 3 = +2 4 6 – 3 = +3 9 7 – 3 = +4 16 Sum (Σ) = 10 [not zero] Sum = 30 Sum of squared differences for 4 = 15 Sum of squared differences for 6 = 15 Sum of squared differences for 7 = 30 True Mean (5) has least sum2 = 10

  10. Interpreting the Mode • Definition: The most frequent value • Especially useful for categorical variables • Focus upon the distribution of values • Applicable to quantitative data through • shape of distribution • Illustrations: heart disease, alcohol consumption, • GDP per capita

  11. Cautionary Tales • Mean is the most common measure of central tendency • It is misleading for variables with skewed distributions • (e.g., power, wealth, education, income) • Mean, median, and mode converge with normal • distributions, and diverge in cases of skewed distributions.

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