Ch03-Statistical-Description-of-Data-商务统计学概论(英文第四版.ppt

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1、CHAPTER 3:Statistical Description of Datato accompanyIntroduction to Business Statisticsfourth edition,by Ronald M.WeiersPresentation by Priscilla Chaffe-Stengel Donald N.Stengel 2002 The Wadsworth GroupChapter 3-Learning ObjectivesDescribe data using measures of central tendency and dispersion:for

2、a set of individual data values,andfor a set of grouped data.Convert data to standardized values.Use the computer to visually represent data.Use the coefficient of correlation to measure association between two quantitative variables.2002 The Wadsworth GroupChapter 3-Key TermsMeasures of Central Ten

3、dency,The CenterMean,population;,sampleWeighted MeanMedianMode(Note comparison of mean,median,and mode)2002 The Wadsworth GroupChapter 3-Key TermsMeasures of Dispersion,The SpreadRangeMean absolute deviationVariance(Note the computational difference between s2 and s2.)Standard deviationInterquartile

4、 rangeInterquartile deviationCoefficient of variation 2002 The Wadsworth GroupChapter 3-Key TermsMeasures of AssociationCoefficient of correlation,rDirection of the relationship:direct(r 0)or inverse(r 0)Strength of the relationship:When r is close to 1 or 1,the linear relationship between x and y i

5、s strong.When r is close to 0,the linear relationship between x and y is weak.When r=0,there is no linear relationship between x and y.Coefficient of determination,r2The percent of total variation in y that is explained by variation in x.2002 The Wadsworth GroupThe Center:MeanMeanArithmetic average=

6、(sum all values)/#of valuesPopulation:=(Sxi)/NSample:=(Sxi)/nBe sure you know how to get the value easily from your calculator and computer softwares.Problem:Calculate the average number of truck shipments from the United States to five Canadian cities for the following data given in thousands of ba

7、gs:Montreal,64.0;Ottawa,15.0;Toronto,285.0;Vancouver,228.0;Winnipeg,45.0 (Ans:127.4)x 2002 The Wadsworth GroupThe Center:Weighted MeanWhen what you have is grouped data,compute the mean using =(Swixi)/SwiProblem:Calculate the average profit from truck shipments,United States to Canada,for the follow

8、ing data given in thousands of bags and profits per thousand bags:Montreal64.0Ottawa 15.0Toronto 285.0$15.00$13.50$15.50 Vancouver 228.0Winnipeg 45.0$12.00$14.00(Ans:$14.04 per thous.bags)2002 The Wadsworth GroupThe Center:ModeThe mode is the most frequent value.While there is just one value for the

9、 mean and one value for the median,there may be more than one value for the mode of a data set.The mode tends to be less frequently used than the mean or the median.2002 The Wadsworth GroupComparing Measures ofCentral TendencyIf mean=median=mode,the shape of the distribution is symmetric.If mode med

10、ian median mode,the shape of the distribution trails to the right,is positively skewed.If mean median median mean,the shape of the distribution trails to the left,is negatively skewed.2002 The Wadsworth GroupKey Concept-ResidualsResiduals are the differences between each data value in the set and th

11、e group mean:for a population,xi for a sample,xi 2002 The Wadsworth GroupThe Spread:VarianceVariance is one of the most frequently used measures of spread,for population,for sample,The right side of each equation is often used as a computational shortcut.2002 The Wadsworth GroupThe Spread:Standard D

12、eviationSince variance is given in squared units,we often find uses for the standard deviation,which is the square root of variance:for a population,for a sample,Be sure you know how to get the values easily from your calculator and computer softwares.2002 The Wadsworth GroupRelative Position-Quarti

13、lesOne of the most frequently used quantiles is the quartile.Quartiles divide the values of a data set into four subsets of equal size,each comprising 25%of the observations.To find the first,second,and third quartiles:1.Arrange the N data values into an array.2.First quartile,Q1=data value at posit

14、ion(N+1)/43.Second quartile,Q2=data value at position 2(N+1)/44.Third quartile,Q3=data value at position 3(N+1)/4 2002 The Wadsworth GroupWhat is a Standardized Value?How far above or below the individual value is compared to the population mean in units of standard deviation“How far above or below”

15、=(data value mean)which is the residual.“In units of standard deviation”=divided by sStandardized data valueA negative z means the data value falls below the mean.2002 The Wadsworth GroupWhy is a Standardized Value Important?Chebyshevs Theorem:For either a sample or a population,the percentage of ob

16、servations that fall within k (for k 1)standard deviations of the mean will be at least 2002 The Wadsworth GroupWhy is a Standardized Value Important?The Empirical Rule:For bell-shaped,symmetric distributions,about 68%of the observations will fall within 1 standard deviation of the mean,about 95%of

17、the observations will fall within 2 standard deviations of the mean,practically all of the observations will fall within 3 standard deviations of the mean.2002 The Wadsworth GroupAn Example:Problem 3.54A law enforcement agency administering breathalyzer tests to a sample of drivers stopped at a New

18、Years Eve roadblock measured the following blood alcohol levels for the 25 drivers who were stopped:0.00%0.08%0.15%0.18%0.02%0.04%0.00%0.03%0.11%0.17%0.05%0.21%0.01%0.10%0.19%0.00%0.09%0.05%0.03%0.00%0.03%0.00%0.16%0.04%0.10%2002 The Wadsworth GroupProblem 3.54,continuedUse Chebyshevs Theorem to det

19、ermine the minimum percentage of observations that should fall within k=1.50 units of standard deviation from the mean.Ans:At least 55.55%of the data values should fall within k=1.50 units of standard deviation from the mean.2002 The Wadsworth GroupProblem 3.54,continuedDo the sample results support

20、 Chebyshevs Theorem?Ans:1.50(s)=0.1026%mean+1.50(s)=0.0736%+0.1026%=0.1762%mean 1.50(s)=0.0736%0.1026%=0.0290%A total of 22/25 data values fall in this interval,or 88%of the sample.Yes,the data support Chebyshevs Theorem.2002 The Wadsworth GroupProblem 3.54,continuedCalculate the coefficient of variation for these data.Ans:2002 The Wadsworth Group