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1、Chapter 4Landmark Summaries:Interpreting Typical Values and Percentiles,Practical Business Statistics,Chapter Topics,Measures of Central TendencyMean, Median, Mode Midrange, Quartiles Exploratory Data AnalysisFive-Number SummaryBox Plot,Summary Measures,Central Tendency,Mean,Median,Mode,Midrange,Int
2、erquartile Range,Midhinge,Summary Measures,Variation,Variance,Standard Deviation,Coefficient of Variation,Range,Measures of Central Tendency,Central Tendency,Mean,Median,Mode,Midrange,Midhinge,Sample Mean,Population Mean,The Arithmetic Average of data values:,The Mean (Arithmetic Average),Sample Mea
3、n,Population Mean,Sample Size,Population Size,The Most Common Measure of Central Tendency Affected by Extreme Values (Outliers),The Mean (continued),0 1 2 3 4 5 6 7 8 9 10,0 1 2 3 4 5 6 7 8 9 10 12 14,Mean = 5,Mean = 6,The Median,Important Measure of Central Tendency In an ordered array, the median
4、is the “middle” number. If n is odd, the median is the middle number. If n is even, the median is the average of the 2 middle numbers.,The Median (continued),0 1 2 3 4 5 6 7 8 9 10,0 1 2 3 4 5 6 7 8 9 10 12 14,Median = 5,Median = 5,Not Affected by Extreme Values For skewed data, represents the “typi
5、cal case” better than the average does,The Mode,A Measure of Central Tendency Value that Occurs Most Often Not Affected by Extreme Values,Mode = 8,0 1 2 3 4 5 6 7 8 9 10 11 12 13,The Mode (continued),There May Not be a Mode There May be Several Modes Used for Either Numerical or Categorical Data,0 1
6、 2 3 4 5 6,No Mode,0 1 2 3 4 5 6,Two Modes,Midrange,A Measure of Central Tendency Average of Smallest and Largest Observation:,Midrange,Midrange (continued),Affected by Extreme Value,0 1 2 3 4 5 6 7 8 9 10,0 1 2 3 4 5 6 7 8 9 10,Midrange = 5,Midrange = 3,Which summary to use?,Average Best for normal
7、 data Preserves totals Median Good for skewed data or data with outliers, provided you do not need to preserve or estimate total amounts Mode Best for categories (nominal data). The mode is the only summary computable for nominal data!,Quartiles,Not a measure of central tendencySplit ordered data in
8、to 4 quarters,25%,25%,25%,25%,Q1,Q2,Q3,Selected landmarks to represent entire data set Median = 50th percentile Quartiles LQ = Lower Quartile = 25th percentileRank = UQ = Upper Quartile = 75th percentile Rank is n+1rank of lower quartile Extremes Smallest = 0th percentile Largest = 100th percentile,
9、Five-Number Summary,Five-Number Summary (continued),Provides information about Central summary Range of the data “Middle half” of the data Skewness,Exploratory Data Analysis,Box Plot Graphical display of data using 5-number summary,Median(Q2),4,6,8,10,12,Q,3,Q,1,X,largest,X,smallest,Spending rank or
10、dered from smallest to largest0.3, 0.6, 0.9, 1.1, 1.4, 2.8, 3.8, 5.51 2 3 4 5 6 7 8LQ is (0.6+0.9)/2 = 0.75 UQ is (2.8+3.8)/2 = 3.3,Example: Spending,Example: Spending (continued),Five-number summary0.3, 0.75, 1.25, 3.3, 5.5 Box plotShows some skewness (lack of symmetry),Exercise,A systems manager i
11、n charge of a companys network keeps track of the number of server failures that occur in a day. The following data represent the number of server failures in a day for the past two weeks.3 0 3 26 2 7 4 0 2 3 3 6 3 Obtain the mode for these data,Solution,The ordered array for these data is: 0 0 1 2
12、2 3 3 3 3 3 4 6 7 26 The most typical value ,or mode, is 3. Thus, the systems manager can say that the most common occurrence is to have three server failures in a day. Note that for this data set the median is equal to 3 and the arithmetic mean is equal to 4.5. The value 26 is an outlier;thus the m
13、edian and the mode is a better description of central tendency than the mean.,Exercise,决策者一旦信奉某种无效的行动方针，常会使自己所犯错误逐步升级。组织行为学家和社会心理学家们对这一逐步升级过程产生强烈兴趣。诸如“沉没成本”效应，“陷进泥沼”效应，以及“投入过多，难以自拔”效应，均属这种现象。不过大多数人则把此种现象看作是“落入陷阱”。今有52名初学心理学的大学生参加一项实验室实验，旨在探究将先出现的结果视作自我同一性（主观与客观的一致性）体现的个人倾向，是否会加强上述落入陷阱效应（Administrative Science Quarterly, May. 1986）。整个实验由30项试验组成，试验中根据学生判断不同形状几何图形的准确性打分，每项试验的总得分见表。计算这个数据集的平均值、中位数和众数（类）这几个集中趋势量度是否出现在数据分布的中心？,Exercise,5 4 7 24 6 12 11 15 11 10 23 4 20 5 45 6 6 15 5 15 10 13 9 4 6,Solution,mean=9.7Median=7Mode=5 b. The answer is yes,
