Lecture05 - Introduction to Statistics Statistics 110,...

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Unformatted text preview: Introduction to Statistics Statistics 110, Spring 2010 Professor Edsel A. Pena E-Mail: pena@stat.sc.edu February 10, 2010 Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 Lecture 05: Numerical Summary Measures Measures of Position: Location, Extreme Values. Mean, Mode, and Modal Class. Five-Number Summary (LV, Q1, Median, Q3, HV). Measures of Variation. Variance and Standard Deviation. Range and Inter-Quartile Range. The BoxPlot : Formal Construction and Outliers. Information from Mean and Standard Deviation (Chebyshevs and Empirical Rules). Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 Motivating Example Our Class Data Set. Variable: Weight. We have discussed some graphical methods of presenting the observations for this variable. Frequency Table and Histogram. BoxPlot. Comparative Boxplots for comparing different groups. To recall, we present these graphical representations. Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 Frequency Histogram for Weight H i s t o g r a m o f W e i g h t W e i g h t Frequency 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 10 20 30 40 Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 BoxPlot for Weight 100 150 200 250 300 B o x P l o t o f V a r i a b l e W e i g h t Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 Comparative BoxPlots: Classified by Gender 0 1 100 150 200 250 300 C o m p a r a t i v e B o x P l o t s Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 Limitations of Graphical Methods Though A Picture Is Worth A Thousand Words, But, we still need A Few (Good) Numbers To Succinctly Summarize the Data Set! Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 Some Questions Pertinent to Summarizing Data Set Where is the CENTER of this data set? Where are the important POSITIONS of this data set? Where are the EXTREMES of this data set? How much VARIATION is there in the data set? How do we INTERPRET measures of position and variation simultaneously? Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 The Measures of Location and Position Summarizing the Center, Location, and Position of a Data Set Professor Edsel A. Pe na E-Mail: pena@stat.sc.edu Introduction to Statistics Statistics 110, Spring 2010 The Mean or Average Value Definition (Descriptive) The mean or average value of a set of observations is equal to the total or sum of the values of the observations divided by the number of observations....
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Lecture05 - Introduction to Statistics Statistics 110,...

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