03/05/2003 Week #2 江支弘 Measuring Center or Average 量度中心或平均 Stemplot: Mean: 平均數 arithmetic average of observations Median: 中位數 middle value of... (in increasing order) 第 (n+1)/2 個 Mode: 眾數 most frequent value among …

03/05/2003 Week #2 江支弘

03/05/2003 Week #2 江支弘 Comparing mean and median 平均值與中位數的比較 Both describe the center of a set of data Mean is strongly influenced by a few extreme values 極端值

03/05/2003 Week #2 江支弘 Measuring Variability or Spread 度量變異性或離度 Highway gas mileage tb4-4<f4-15 Quartiles 四分位數 : measuring spread First quartile Q 1 : the median of the observations to the left of the overall median Third quartile Q 3 : the median of the observations to the right of the overall median 中間一半資料的離度  由 Q 1 與 Q 3 來觀察

03/05/2003 Week #2 江支弘

03/05/2003 Week #2 江支弘

03/05/2003 Week #2 江支弘 Five-number summary 五數綜合 In symbols, the five-number summary is Minimum Q 1 M 中位數 Q 3 Maximum Boxplot 盒圖 : ex19, p170

03/05/2003 Week #2 江支弘

03/05/2003 Week #2 江支弘 Variance and standard deviation 變異數與標準差 Standard deviation: measuring spread Variance Standard deviation s is the square root of s 2 Ex calculating s Ex

03/05/2003 Week #2 江支弘 Properties of standard deviation 標準差的性質 s measures spread about the mean x use s for spread only when x (or x bar ) is used for center 標準差度量以平均值為中心的離度 s = 0 only if no spread Otherwise s > 0 More spread out of observations  s gets larger s and x are both strongly influenced by extremes

03/05/2003 Week #2 江支弘 Choosing numerical descriptions 選擇適當的數值描述方式 Five-number summary is usually better than the mean and standard deviation for describing a skewed distribution 偏斜分佈 Use x and s for reasonably symmetric distributions 合理對稱的分佈

03/05/2003 Week #2 江支弘 Composite Summary Measures

03/05/2003 Week #2 江支弘 Composite Summary Measures

03/05/2003 Week #2 江支弘 Summary Statistical Measures: The Proportion Example, p61