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Unformatted text preview: Introduction to Statistics Statistics 110, Spring 2010 Professor Edsel A. Pe˜na EMail: [email protected] February 10, 2010 Professor Edsel A. Pe˜ na EMail: [email protected] Introduction to Statistics Statistics 110, Spring 2010 Lecture 05: Numerical Summary Measures ▶ Measures of Position: Location, Extreme Values. ▶ Mean, Mode, and Modal Class. ▶ FiveNumber Summary (LV, Q1, Median, Q3, HV). ▶ Measures of Variation. ▶ Variance and Standard Deviation. ▶ Range and InterQuartile Range. ▶ The BoxPlot : Formal Construction and Outliers. ▶ Information from Mean and Standard Deviation (Chebyshev’s and Empirical Rules). Professor Edsel A. Pe˜ na EMail: [email protected] 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 EMail: [email protected] 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 EMail: [email protected] 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 EMail: [email protected] 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 EMail: [email protected] 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 EMail: [email protected] 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 EMail: [email protected] 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 EMail: [email protected] 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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This note was uploaded on 06/13/2011 for the course STAT 110 taught by Professor Johnson during the Spring '07 term at South Carolina.
 Spring '07
 JOHNSON
 Statistics

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