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 observatio

nsMedian: 中位數middle value of ... (in increasin

g 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 dataMean is strongly influenced by a few extre

me 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 Q1: the median of the observations to the left of the overall median

Third quartile Q3 : the median of the observations to the right of the overall median

中間一半資料的離度 由 Q1 與 Q3 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 Q1 M中位數 Q3 Maximum

Boxplot 盒圖 : ex19, p170<f4-16>

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 spreadVariance

Standard deviation s is the square root of s2

Ex calculating s

1

)()()( 222

212

n

xxxxxxs n

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 largers 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

複合式度量

Composite Summary Measures

03/05/2003 Week #2 江支弘

Summary Statistical Measures: The Proportion

Example, p61