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Lectures 3-4 Week2 • Describing Data with Numerical Values • (Chapter 2) 5/24/2017 Chapter 2 1 Terminology and Types of Measures • Measures associated to Population: Parameters • Measures associated to a sample: Statistics Population 5/24/2017 Chapter 2 Sample 2 Two kinds of measures • Measures of Location, center, position • Measures of dispersion, shape, variability 5/24/2017 Chapter 2 3 Measures of location • The mean – Example • The median – Example • The mode – Example 5/24/2017 Chapter 2 4 Relationship between mean and median • • • • Median is robust If data symmetric, mean=median If right-skewed data, mean shifts to right If left-skewed data, mean shifts to left. Median unchanged. 5/24/2017 Chapter 2 5 Measures of Dispersion • Range – Example • Variance – Shortcut formula – Example • Standard deviation – Example Advantage: has same unit as data. 5/24/2017 Chapter 2 6 Practical significance of standard deviation • Chebychev’s Theorem – Example • Empirical rule (symmetric data) – Example • Measures of relative standing – Z-score, Outliers – Example 5/24/2017 Chapter 2 7 Quartiles, Box-plots • • • • • • • Q1=1st quartile Q2=median Q3=3rd quartile IQR=Q3-Q1 Computing Formulae and Examples Box-plot Outliers 5/24/2017 Chapter 2 8