应用统计学英文课件BusinessStatisticsCh03NumericalDescriptiveMeasures.ppt
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1、Business Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-1Chapter 3Numerical Descriptive MeasuresBusiness Statistics:A First CourseFifth EditionChoice is yours,part 2Business Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-3In this chapter,you learn:nTo describe the properties
2、of central tendency,variation,and shape in numerical datanTo calculate descriptive summary measures for a populationnTo construct and interpret a boxplotnTo calculate the covariance and the coefficient of correlationLearning ObjectivesBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap
3、 3-4Summary DefinitionsThe central tendency is the extent to which all the data values group around a typical or central value.The variation is the amount of dispersion,or scattering,of values The shape is the pattern of the distribution of values from the lowest value to the highest value.Business
4、Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-5Measures of Central Tendency:The MeannThe arithmetic mean(often just called“mean”)is the most common measure of central tendencynFor a sample of size n:Sample sizenXXXnXXn21n1iiObserved valuesThe ith valuePronounced x-barMeasures of Central
5、 Tendency:The MeannExample volume of Coke Listed below are the volumes(in ounces)of the Coke in five different cans.Find the mean for this sample.12.3 12.1 12.2 12.3 12.2oz.12.22 is emean volum The22.1252.123.122.121.123.12nxxBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-7Measu
6、res of Central Tendency:The MeannThe most common measure of central tendencynMean=sum of values divided by the number of valuesnAffected by extreme values(outliers)(continued)0 1 2 3 4 5 6 7 8 9 10Mean=3 0 1 2 3 4 5 6 7 8 9 10Mean=4351555432145205104321Business Statistics:A First Course,5e 2009 Pren
7、tice-Hall,Inc.Chap 3-8Measures of Central Tendency:Locating the MediannThe location of the median when the values are in numerical order(smallest to largest):nIf the number of values is odd,the median is the middle numberdataorderedtheinposition21npositionMedianBusiness Statistics:A First Course,5e
8、2009 Prentice-Hall,Inc.Chap 3-9Measures of Central Tendency:Locating the MediannIf the number of values is even,the median is the average of the two middle numbersNote that is not the value of the median,only the position of the median in the ranked data21nBusiness Statistics:A First Course,5e 2009
9、Prentice-Hall,Inc.Chap 3-10Measures of Central Tendency:The MediannIn an ordered array,the median is the“middle”number(50%above,50%below)nNot affected by extreme values0 1 2 3 4 5 6 7 8 9 10Median=3 0 1 2 3 4 5 6 7 8 9 10Median=3Business Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-11M
10、easures of Central Tendency:The ModenValue that occurs most oftennNot affected by extreme valuesnUsed for either numerical or categorical datanThere may be no modenThere may be several modes0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode=90 1 2 3 4 5 6No ModeMeasures of Central Tendency:The Moden Mean Mode
11、ModeBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-13Measures of Central Tendency:Review ExampleHouse Prices:$2,000,000$500,000$300,000$100,000$100,000Sum$3,000,000Mean:($3,000,000/5)=$600,000Median:middle value of ranked data =$300,000Mode:most frequent value =$100,000Business
12、Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-14Measures of Central Tendency:Which Measure to Choose?The mean is generally used,unless extreme values(outliers)exist.The median is often used,since the median is not sensitive to extreme values.For example,median home prices may be reporte
13、d for a region;it is less sensitive to outliers.In some situations it makes sense to report both the mean and the median.Business Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-15Measures of Central Tendency:SummaryCentral TendencyArithmetic MeanMedianModenXXnii1Middle value in the order
14、ed arrayMost frequently observed valueBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-16Same center,different variationMeasures of VariationnMeasures of variation give information on the spread or variability or dispersion of the data values.VariationStandard DeviationCoefficient
15、 of VariationRangeVarianceBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-17Measures of Variation:The RangeSimplest measure of variationDifference between the largest and the smallest values:Range=Xlargest Xsmallest0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Range=13-1=12Example:Business
16、Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-18Measures of Variation:Why The Range Can Be MisleadingIgnores the way in which data are distributedSensitive to outliers7 8 9 10 11 12Range=12-7=57 8 9 10 11 12Range=12-7=51,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,51,1,1,1,1,1,1,1,1,1
17、,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120Range=5-1=4Range=120-1=119Business Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-19nAverage(approximately)of squared deviations of values from the meannSample variance:Measures of Variation:The Variance1-n)X(XSn1i2i2Where =arithmetic meann=sample sizeXi=i
18、th value of the variable XXBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-20Measures of Variation:The Standard DeviationnMost commonly used measure of variationnShows variation about the meannIs the square root of the variancenHas the same units as the original datanSample stand
19、ard deviation:1-n)X(XSn1i2iBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-21Measures of Variation:The Standard DeviationSteps for Computing Standard Deviation1.Compute the difference between each value and the mean.2.Square each difference.3.Add the squared differences.4.Divide
20、this total by n-1 to get the sample variance.5.Take the square root of the sample variance to get the sample standard deviation.Business Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-22Measures of Variation:Sample Standard DeviationSample Data (Xi):10 12 14 15 17 18 18 24 n=8 Mean=X=164
21、.309571301816)(2416)(1416)(1216)(101n)X(24)X(14)X(12)X(10S22222222A measure of the“average”scatter around the meanVariance of the Getting-Ready TimeBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-24Measures of Variation:Comparing Standard DeviationsMean=15.5 S=3.338 11 12 13 14 1
22、5 16 17 18 19 20 2111 12 13 14 15 16 17 18 19 20 21Data BData AMean=15.5 S=0.92611 12 13 14 15 16 17 18 19 20 21Mean=15.5 S=4.570Data CBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-25Measures of Variation:Comparing Standard DeviationsSmaller standard deviationLarger standard de
23、viationBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-26Measures of Variation:Summary CharacteristicsThe more the data are spread out,the greater the range,variance,and standard deviation.The more the data are concentrated,the smaller the range,variance,and standard deviation.If
24、 the values are all the same(no variation),all these measures will be zero.None of these measures are ever negative.Business Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-27Measures of Variation:The Coefficient of VariationnMeasures relative variationnAlways in percentage(%)nShows varia
25、tion relative to meannCan be used to compare the variability of two or more sets of data measured in different units 100%XSCVBusiness Statistics:A First Course,5e 2009 Prentice-Hall,Inc.Chap 3-28Measures of Variation:Comparing Coefficients of VariationnStock A:nAverage price last year=$50nStandard d
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