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1、初階應用統計 Summer 2004,授課教師：統計系余清祥日期：2004年7月13日 第三週：統計圖表、機率概論 課程下載：http:/csyue.nccu.edu.tw,統計圖表(Table and Figure),除了敘述統計量外，圖形與表格經常可提供更多、更詳細的訊息。 (A picture is worth a thousand words.)使用圖表時需注意適用時機與限制。,Frequency Distribution(出現頻率),A frequency distribution is a tabular summary of data showing the frequency
2、(or number) of items in each of several nonoverlapping classes. The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data.,Example 1: Hudson Auto Repair,The manager of Hudson Auto would like to have a better understanding of the cost of
3、parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed below.,Tabular Summary (Frequencies and Percent Frequencies)Parts PercentCost ($) Frequency Frequency50-59 2 460-69 13 2670-79 16 328
4、0-89 7 1490-99 7 14100-109 5 10Total 50 100,Crosstabulation (Contingency Table；列聯表),Crosstabulation is a tabular method for summarizing the data for two variables simultaneously. Crosstabulation can be used when:One variable is qualitative and the other is quantitativeBoth variables are qualitativeB
5、oth variables are quantitative The left and top margin labels define the classes for the two variables.,Example 2: Finger Lakes Homes,The number of Finger Lakes homes sold for each style and price for the past two years is shown below.Price Home Style Range Colonial Ranch Split A-Frame Total $99,000
6、 12 14 16 3 45Total 30 20 35 15 100,Character Stem-and-Leaf Display,MTB stem c1 (枝葉圖) Stem-and-leaf of C1 N = 30 Leaf Unit = 1.01 3 92 4 33 4 74 5 05 5 711 6 000224(5) 6 5678914 7 01211 7 5668 8 00444 8 882 9 14,MTB boxplot c1 (箱型圖),Boxplot produces a boxplot (also called box-and-whisker plot). A de
7、fault boxplot consists of a box, whiskers, and outliers. Minitab draws a line across the box at the median. By default, the bottom of the box is at the first quartile (Q1) and the top is at the third quartile (Q3). The whiskers are the lines that extend from the top and bottom of the box to the adja
8、cent values, the lowest and highest observations still inside the region defined by the lower limit Q1 - 1.5 (Q3 - Q1) and the upper limit Q1 + 1.5 (Q3 - Q1). Outliers are points outside the lower and upper limits, plotted with asterisks (*). Here is a simple boxplot using the Pulse data, and specif
9、ying Pulse2 in Y and Sex in X, then clicking OK:,MTB histogram c1 (直方圖),Histogram of Example 1,Parts Cost ($),2,4,6,8,10,12,14,16,18,Frequency,50 60 70 80 90 100 110,Ogive with Cumulative Percent Frequencies,Parts Cost ($),20,40,60,80,100,Cumulative Percent Frequency,50 60 70 80 90 100 110,Example 3
10、: Marada Inn,Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are shown below.,Below Average Average Above Average Above Average Above Average Above Av
11、erage ,Bar Graph(長條圖),Pie Graph(圓餅圖),Scatter Diagram(散佈圖),No Apparent Relationship,A Positive Relationship,A Negative Relationship,Tabular and Graphical Procedures,Data,Qualitative Data,Quantitative Data,Tabular Methods,Tabular Methods,GraphicalMethods,GraphicalMethods,FrequencyDistribution Rel. Fre
12、q. Dist. % Freq. Dist. Crosstabulation,Bar Graph Pie Chart,FrequencyDistribution Rel. Freq. Dist. Cum. Freq. Dist. Cum. Rel. Freq.Distribution Stem-and-LeafDisplay Crosstabulation,Dot Plot Histogram Ogive ScatterDiagram,圖形、表格操作範例,以統計系學生對商學院學生的滿意度調查為例，檔案為NCCUcommerce(2002).mtw。將展示以下事項： 敘述統計量 繪製圖形 整理資
13、料、製成表格,機率與條件機率,Probability as a Numerical Measure of the Likelihood of Occurrence,0,1,.5,Increasing Likelihood of Occurrence,Probability:,The occurrence of the event isjust as likely as it is unlikely.,隨機實驗(Random Experiment),隨機實驗為不能確定地預測結果(Outcome)的實驗。 等待下一班公車的時間 應用統計的期中考成績 嬰兒的出生日期(或體重) 本班同學今天衣服的顏色
14、,樣本空間(Sample Space),樣本空間通常以 S表示，代表隨機實驗的所有可能結果。 等待時間的樣本空間為 0到 期中考成績的樣本空間為0到100分 嬰兒出生日期的樣本空間為一月一日至十二月三十一日 衣服顏色的樣本空間為紅、橙、,事件(Event):, 樣本空間的部份集合(以大寫英文字母表示) (e.g. A=期中考及格(相當於60到100分) 1. : 空事件(Null Event) 不含任何樣本點 2. : A與B的聯事件(Union Event) 3. : A與B的交事件(Intersection Event) 4. A(或 )：A的餘事件(Complementary Event
15、) 5. 若 則A與B不能同時發生，即A與B為互斥事件,機率的定義:,(1) , (2) (3) 若 ( 為互斥事件), 則,Another useful counting rule enables us to count the number of experimental outcomes when n objects are to be selected from a set of N objects. Number of combinations of N objects taken n at a timewhere N! = N(N - 1)(N - 2) . . . (2)(1)n! = n(n - 1)( n - 2) . . . (2)(1)0! = 1,
