1. Chapter 2 Frequency Distributions 次數分配
Statistics
Chapter 2
Frequency Distributions
次數分配

2. 資料整理 How do we turn “a bunch of numbers” into something meaningful?
整理資料的第一步驟
統計表
統計圖

3. 統計表 內容
標題 (Title)
表身 (Body)
資料來源及附註

5. 統計圖 種類 條圖 (bar chart) 餅圖 (pie chart) 直方圖 (histogram) 多邊圖 (polygon)
枝葉圖 (stem-and-leaf display)

6. 次數分配 Frequency Distributions
最基本的統計方法
依據資料原始分數按照大小，發生次數予以分類，以利觀察分析&解釋。
Frequency distribution table (表)
Frequency distribution chart (圖)

7. 次數分配 for categorical data
依照類別分類，計算各組次數，顯示資料分佈情形
次數分配基本統計值 類別
次數 frequency
相對次數 proportion
百分比 percentage

8. Frequency distribution table (cont’)
Table 1 Frequency distribution of the Pilot Study Sample (N=117)
Category
Frequency
(f)
Percentage %
Cumulative
Percentage(%)
Gender
Male
Female
Sub total 57 60
117
48.7
51.3
100
Industry experience
Yes No 07 10
91.5
8.5
If yes, length of industry experience (n=107)
Less than one year
1~ less than 2 years
2~ less than 3 years
more than 3 years 24 35 38
107
22.3
32.8
35.5
9.3
55.1
90.6

9. Raw data 20 個學生(N=20) 考試成績 (滿分10分) 8 9 8 7 10 9 6 4 9 8

15. 次數分配 for continuous data
連續資料的次數分配
需將資料加以歸類以便讀者能一目了然資料分配狀況
將連續資料分成若干組，計算各組次數
原始組數
rows=highest – lowest + 1
將原始組數縮減到較易manage的組數
分組原則
決定組數 10組
決定組距 (interval width) 大小為 2，5 或 10的倍數
Each interval should start with a score that is a multiple of the width
All interval should be the same width

16. 排序
全距 (range)
決定組數 (# of interval)
組距 (interval width) = 全距/組數
決定組限(real limit)

17. Example 2.3
25位學生成績 (N=25)

18. 最低 53 最高 94 全距= 94-53=41 組數= = 5 組距=41/5=8.2  10 區間組限 X f %排序
全距 (range)
決定組數 (# of interval)
組距 (interval width) = 全距/組數
決定區間組限(real limit)
最低 53 最高 94
全距= 94-53=41
組數= = 5
組距=41/5=8.2  10
區間組限
X f %
Total

19. Real limits vs. Apparent limits
Continuous variable creates continuous data
Infinite numbers
Real limits 區間組限
界定出continuous data的上下界
Upper real limit
Lower real limit
Real limits vs. Apparent limits

20. Apparent limit
Lower real limit
Upper real limit

21. Exercise 30位學生體重
N=30

22. 組別 組限 組界
組中點 f %
c.p 1
30-34 32 3 2
35-39 37 7 10
40-44 42 4 13 23
45-49 47 33 5
50-54 52 17 50 6
55-59 57 63
60-64 62 73 8
65-69 67 20 93 9
70-74 72
100 30

24. Histogram 直方圖 適用於 continuous data 以呈現出連續資料的特質
Difference between a bar chart and a histogram:
Bar chart: distances between each bar.
Histogram: no distance among bars.
Bar chart is for categorical data

25. Histogram

26. 多邊圖 polygon

27. Stem-and-Leaf Displays
An alternative to histograms
Display distributions using actual data values
Advantage is that no information is lost since all values are shown
Stem-first digit of each number
Leaf-second digit

28. Stem-and-leaf example
English test scores:

29. 3 4 5 6 7 8 9
2 0 7 3
6 7
8 3 2 3 4 5 6 7 8 9
0 2
6 7
2 3 8
重將leaves
按照次序排好
OK!

30. 3 4 5 6 7 8 9
0 2
6 7
2 3 8 3 4 5 6 7 8 9
2 3 8
0 2
6 7

31. Exercise

32. Example of Histogram

33. 資料的圖形分佈 Data distribution
資料分佈的三種特質
Shape 資料分佈形狀
Symmetrical distribution
Skewed distribution
Central tendency 資料集中趨勢 峰度
Variability資料散佈狀態

34. 資料形狀 Skewed distributions 不對稱分佈 Symmetric distributions 對稱分佈
are similar on both sides of the center
Skewed distributions 不對稱分佈
do not look the same on both sides of the center
Positive skew 右偏
Negative skew 左偏

35. Degree of skewness displayed by a histogram

36. 資料集中趨勢 當次數分配有集中的趨勢: 峰度 (Modality) 峰度高低平坦 Unimodal distributions 單峰
Multimodal distributions 多峰
峰度高低平坦
Distributions can be described as flat (platykurtic), peaked (leptokurtic), or normal (mesokurtic)
常態峰度 mesokurtosis
高狹峰 leptokurtosis
低闊峰 platykurtosis

37. Modality displayed by a histogram

38. Distributional Spread
Any distribution of scores can be described in terms of its spread or dispersion
Kurtosis is another term associated with the spread or peakedness of the data

39. Illustration of degree of spread