STAT6202_coursenotes_1112

# STAT6202_coursenotes_1112 - Contents 1 Data Summary and...

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Unformatted text preview: Contents 1 Data Summary and Presentation 4 1.1 Populations and Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Reasons for Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Random Sample from a Finite Population . . . . . . . . . . . . . . . . . . . . . 4 1.1.3 How to obtain a random sample . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Types of variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Tables and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.1 Presentation of Qualitative Data (ordered and unordered) . . . . . . . . . . . . 5 1.3.2 Presentation of Discrete Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.3 Presentation of Small Amounts of Continuous Data . . . . . . . . . . . . . . . 7 1.3.4 Symmetric and Skew Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.5 Presentation of Large Amounts of Continuous Data . . . . . . . . . . . . . . . 8 1.3.6 Comments on Dotplots, Stemplots, Histograms and Boxplots . . . . . . . . . . 10 1.4 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4.1 Measures of Location (or Level) . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4.2 Measures of spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Five-figure summaries and boxplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Choice of Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.7 Change of origin and scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.8 Log transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Describing bivariate data 16 2.1 From Univariate to Bivariate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.2 An illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.3 Linear transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Principle of least squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.1 Fitting a constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.2 Fitting a straight line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Properties of the correlation coeﬃcient . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1 2.4 Rank correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 The Normal Distribution 24 3.1 Population distribution and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.33....
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STAT6202_coursenotes_1112 - Contents 1 Data Summary and...

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