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Chapter 3

Chapter 3. Numerical Descriptive Measures. Properties of Numerical Data. 3 major properties that describe a set of numerical data Central tendency (what’s the central value?) Variation (how spread out are the data?) Shape (what’s the pattern?) Unusual or outlying members of a data set

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Chapter 3

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  1. Chapter 3 Numerical Descriptive Measures

  2. Properties of Numerical Data • 3 major properties that describe a set of numerical data • Central tendency (what’s the central value?) • Variation (how spread out are the data?) • Shape (what’s the pattern?) • Unusual or outlying members of a data set • More precise than graphs—often need more than the visual.

  3. 3.1 Measures of Central Tendency, Variation, and Shape Central Tendency • Arithmetic mean (formula 3.1) • Median (formula 3.2) • Mode • Geometric mean (formula 3.5)

  4. More on Central Tendency Quartiles (Q1, Q2, Q3) • Q1 , Q3 Non-central location • Splits data set into quarters

  5. variation Variation • Definition • Range (formula 3.7) • Interquartile range (formula 3.8) • Variance and standard deviation (3.9 & 3.10) • Coefficient of variation (formula 3.11)

  6. Z scores • Formula 3.12 • (observed – expected) / approp. Variation • interpretation

  7. shape • Skewness • Skewed • Symmetrical

  8. Statistics Output • Excel • Tools, Data Analysis, Descriptive Statistics • Minitab

  9. Page 96: Empirical Rule • Variability of bell shaped distributions • ≈ 68% of values fall within ± 1 std dev. of mean • ≈ 95% of values fall within ± 1 std dev. of mean • ≈ 99.7% of values fall within ± 1 std dev. of mean

  10. Page 102-3: Five-Number Summary • The five number summary is a well-known method of examining shape. • The five number summary is used to create the Box-and-Whisker plot. • Ignore Table 3.9 • Use minitab or phstat. • Note Figure 3.5.

  11. Page 108-9: Coefficient of Correlation • Related to scattergram. • “ρ” and “r” • Figure 3.9 is excellent! • Calculation: do not use formula 3.19! Use excel if necessary.

  12. 3.6: Pitfalls in Numerical Descriptive Measures and Ethical Issues • Analysis should be objective. Be thorough. • Interpretation is subjective. Be fair and clear. • Ethical issues come up when you try to decide what to report. Intentionally choosing inappropriate measures is unethical. As is distorting facts and selective reporting.

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