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WMU STAT 2160 - Location and Spread of numerical data

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Measure of Central TendencyLocation or Central TendencyMeasure of VariationSpread or VariationSome Rulesabout Data ChangeShape of DistributionOverall ShapeShape of Middle Half of DataEmpirical Rulefor normal distributionMeasure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleChapter 3. Location and Spreadof numerical dataJ.C. WangJC Wang (WMU) Stat2160 S2160, Chapter 3 1 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleGoal and Objectiveof Chapter 3To learn about the location and spread properties of numericaldataJC Wang (WMU) Stat2160 S2160, Chapter 3 2 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleiClicker Question 3.1 Pre-lectureiClicker Question 3.1 Pre-lectureJC Wang (WMU) Stat2160 S2160, Chapter 3 3 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleOutline1Measure of Central TendencyLocation or Central Tendency2Measure of VariationSpread or Variation3Some Rulesabout Data Change4Shape of DistributionOverall ShapeShape of Middle Half of Data5Empirical Rulefor normal distributionJC Wang (WMU) Stat2160 S2160, Chapter 3 4 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleOutline1Measure of Central TendencyLocation or Central Tendency2Measure of VariationSpread or Variation3Some Rulesabout Data Change4Shape of DistributionOverall ShapeShape of Middle Half of Data5Empirical Rulefor normal distributionJC Wang (WMU) Stat2160 S2160, Chapter 3 5 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocation or Central TendencyNon-resistant Measures— measures affected by (non-resistent to) extreme observationsMean (i.e., average):x =Pni=1xin=x1+ ··· + xnnMidrange:MR =xmin+ xmax2JC Wang (WMU) Stat2160 S2160, Chapter 3 6 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocation or Central TendencyNon-resistant Measures— measures affected by (non-resistent to) extreme observationsMean (i.e., average):x =Pni=1xin=x1+ ··· + xnnMidrange:MR =xmin+ xmax2JC Wang (WMU) Stat2160 S2160, Chapter 3 6 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocation or Central TendencyResistant Measures— measures not affected by extreme observations; i.e., measuresresistent to extreme observationsMedian: value of middle observation when data are orderedMode (or peaked value): most frequently occurred value; datamay have no mode, unique mode, or multiple modes (eg., popularshoe sizes)Midhinge:MH =Q1+ Q32JC Wang (WMU) Stat2160 S2160, Chapter 3 7 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocation or Central TendencyResistant Measures— measures not affected by extreme observations; i.e., measuresresistent to extreme observationsMedian: value of middle observation when data are orderedMode (or peaked value): most frequently occurred value; datamay have no mode, unique mode, or multiple modes (eg., popularshoe sizes)Midhinge:MH =Q1+ Q32JC Wang (WMU) Stat2160 S2160, Chapter 3 7 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocation or Central TendencyResistant Measures— measures not affected by extreme observations; i.e., measuresresistent to extreme observationsMedian: value of middle observation when data are orderedMode (or peaked value): most frequently occurred value; datamay have no mode, unique mode, or multiple modes (eg., popularshoe sizes)Midhinge:MH =Q1+ Q32JC Wang (WMU) Stat2160 S2160, Chapter 3 7 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocationSummer II Quiz Data (sample size n = 14)order score1 82 113 134 195 216 237 258 259 2510 2811 3112 3513 3914 47total 350Mean: x = 350/14 = 25Midrange: MR =xmin+xmax2=8+472= 27.5Median: .5(n + 1) = 7.5,MED =x(7)+x(8)2=25+252= 25Mode: 25Quartiles (TI calculator):n = 14 is even;n2= 7 is odd; the middle value of eachhalf is7+12= 4th valueQ1= x(4)= 19 (4th value from low end)Q3= x(11)= 31 (4th value from high end)Midhinge: MH =Q1+Q32=19+312= 25JC Wang (WMU) Stat2160 S2160, Chapter 3 8 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocationSummer II Quiz Data (sample size n = 14)order score1 82 113 134 195 216 237 258 259 2510 2811 3112 3513 3914 47total 350Mean: x = 350/14 = 25Midrange: MR =xmin+xmax2=8+472= 27.5Median: .5(n + 1) = 7.5,MED =x(7)+x(8)2=25+252= 25Mode: 25Quartiles (TI calculator):n = 14 is even;n2= 7 is odd; the middle value of eachhalf is7+12= 4th valueQ1= x(4)= 19 (4th value from low end)Q3= x(11)= 31 (4th value from high end)Midhinge: MH =Q1+Q32=19+312= 25JC Wang (WMU) Stat2160 S2160, Chapter 3 8 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocationSummer II Quiz Data (sample size n = 14)order score1 82 113 134 195 216 237 258 259 2510 2811 3112 3513 3914 47total 350Mean: x = 350/14 = 25Midrange: MR =xmin+xmax2=8+472= 27.5Median: .5(n + 1) = 7.5,MED =x(7)+x(8)2=25+252= 25Mode: 25Quartiles (TI calculator):n = 14 is even;n2= 7 is odd; the middle value of eachhalf is7+12= 4th valueQ1= x(4)= 19 (4th value from low end)Q3= x(11)= 31 (4th value from high end)Midhinge: MH =Q1+Q32=19+312= 25JC Wang (WMU) Stat2160 S2160, Chapter 3 8 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocationSummer II Quiz Data (sample size n = 14)order score1 82 113 134 195 216 237 258 259 2510 2811 3112 3513 3914 47total 350Mean: x = 350/14 = 25Midrange: MR =xmin+xmax2=8+472= 27.5Median: .5(n + 1) = 7.5,MED =x(7)+x(8)2=25+252= 25Mode: 25Quartiles (TI calculator):n = 14 is even;n2= 7 is odd; the middle value of eachhalf is7+12= 4th valueQ1= x(4)= 19 (4th value from low end)Q3= x(11)= 31 (4th value from high end)Midhinge: MH =Q1+Q32=19+312= 25JC Wang (WMU) Stat2160 S2160, Chapter 3 8 / 36Measure of Central Tendency Measure of Variation Some Rules Shape of Distribution Empirical RuleLocationSummer II Quiz Data (sample size n = 14)order score1 82 113 134 195 216 237 258 259 2510 2811 3112 3513 3914 47total 350Mean: x = 350/14 = 25Midrange: MR =xmin+xmax2=8+472= 27.5Median: .5(n + 1) = 7.5,MED =x(7)+x(8)2=25+252= 25Mode: 25Quartiles (TI calculator):n =


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