1 complete business statistics by amir d. aczel & jayavel sounderpandian 7 th edition. prepared...

1

COMPLETE BUSINESS

STATISTICSbyby

AMIR D. ACZELAMIR D. ACZEL&&

JAYAVEL SOUNDERPANDIANJAYAVEL SOUNDERPANDIAN77thth edition. edition.

Prepared by Prepared by Lloyd Jaisingh, Morehead State UniversityLloyd Jaisingh, Morehead State University

2

Using Statistics 使用統計 Percentiles and Quartiles 百分位數與四分位數 Measures of Central Tendency 集中傾向之衡量 Measures of Variability 變異性之衡量 Grouped Data and the Histogram 群聚數據與直方圖 Skewness and Kurtosis 偏態與峰態 Relations between the Mean and Standard Deviation

Methods of Displaying Data Exploratory Data Analysis 探索性資料分析 Using the Computer 使用電腦

Introduction and Descriptive Statistics1

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Distinguish between qualitative data and quantitative data.

Describe nominal, ordinal, interval, and ratio scales of measurements.

Describe the difference between population and sample. Calculate and interpret percentiles and quartiles. Explain measures of central tendency and how to

compute them. Create different types of charts that describe data sets. Use Excel templates to compute various measures and

create charts.

LEARNING OBJECTIVESAfter studying this chapter, you should be able toAfter studying this chapter, you should be able to::

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Statistics is a science that helps us make better decisions in business and economics as well as in other fields.

Statistics teaches us how to summarize, analyze, and draw meaningful inferences from data that then lead to improve decisions.

These decisions that we make help us improve the running, for example, a department, a company, the entire economy, etc.

WHAT IS STATISTICSWHAT IS STATISTICS??

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1-1. Using Statistics (Two Categories)

Inferential Statistics

推論統計 Predict and forecast values

of population parameters Test hypotheses about

values of population parameters

Make decisions

Descriptive Statistics

敘述統計 Collect Organize Summarize Display Analyze

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Qualitative 定性 - Categorical or Nominal: Examples are- Color 顏色 Gender 性別 Nationality 國籍

Quantitative 定量 - Measurable or Countable: Examples are- Temperatures 溫度 Salaries 薪水 Number of points scored

on a 100 point exam

Types of Data - Two Types (p.4)

7

Scales of Measurement (p.4-5)

衡量尺度定義特色可衡量變數

名目尺度用以辨識或歸類個案之數值

(1) 僅名目本身有意義，數字大小無意義。(2) 是層級最低之尺度，無法轉換為其他尺度。(3) 僅能命名，不能排序。

性別、職業、居住區域、身分證碼、學號等。

順序尺度用以表示等級或順序之數值

(1) 只能指出等級或順序，但無法衡量等級間之差異程度。(2) 可降低為名目尺度。(3) 僅能排序，不能加減。

名次、排序、百分位序等。

區間尺度用以表示程度上差異之數值

(1) 具任意原點， 0 不代表「無」。(2) 可降低為順序尺度及名目尺度。(3) 僅能加減，不能乘除。

溫度、態度、滿意度、同意度、重要性等。

比率尺度用以衡量實質上差異之數值

(1) 具絕對原點， 0 代表「無」。(2) 可降低為區間尺度順序尺度及名目尺度等。(3) 能乘除。

所得、銷售額、考試分數、玉米收穫量等。

Categorical or nonmertric type• Nominal scale ( 名目尺度 ) • Ordinal scale ( 順序尺度 )

Analytical or metric type• Interval scale ( 區間尺度 )• Ratio scale ( 比率尺度 )

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A population( 母體 ) consists of the set of all measurements for which the investigator is interested.

A sample( 樣本 ) is a subset of the measurements selected from the population.

A census( 普查 ) is a complete enumeration of every item in a population.

Samples and Populations( 樣本與母體 )P.5

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Sampling( 抽樣 ) from the population is often done randomly( 隨機 ), such that every possible sample of equal size (n) will have an equal chance of being selected.

A sample selected in this way is called a simple random sample or just a random sample.

A random sample allows chance to determine its elements.

Simple Random Sample

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Population (N) Sample (n)

Samples and Populations

11

Census( 普查 ) of a population may be:Impossible( 不可能 ) Impractical( 不實際 )Too costly( 成本高 )

Why Sample?

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Exercise (p.8, 5min)

• 1-1

• 1-4

• 1-5

13

Given any set of numerical observations, order them according to magnitude.

The Pth percentile in the ordered( 已排序 ) set is that value below which lie P% (P percent) of the observations in the set.

The position of the Pth percentile is given by (n + 1)P/100, where n is the number of observations in the set.

1-2 Percentiles( 百分位數 ) and Quartiles( 四分位數 )

14

A large department store collects data on sales made by each of its salespeople. The number of sales made on a given day by each of 2020 salespeople is shown on the next slide. Also, the data has been sorted in magnitude.

Example 1-2 (p.9)

15

Example 1-2 (Continued) - Sales and Sorted Sales

Sales Sorted Sales

9 6 6 9 12 1010 1213 1315 1416 1414 1514 1616 1617 1616 1724 1721 1822 1818 1919 2018 2120 2217 24

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Find the 50th, 80th, and the 90th percentiles of this data set. To find the 50th percentile, determine the data point in position (n + 1)P/100 = (20 + 1)(50/100) = 10.5. Thus, the percentile is located at the 10.5th position. The 10th observation is 16, and the 11th observation is also 16. The 50th percentile will lie halfway between the 10th and 11th values and is thus 16.

Example 1-2 (Continued) Percentiles

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To find the 80th percentile, determine the data point in position (n + 1)P/100 = (20 + 1)(80/100) = 16.8. Thus, the percentile is located at the 16.8th position. The 16th observation is 19, and the 17th observation is also 20. The 80th percentile is a point lying 0.8 of the way from 19 to 20 and is thus 19.8.


18

To find the 90th percentile, determine the data point in position (n + 1)P/100 = (20 + 1)(90/100) = 18.9. Thus, the percentile is located at the 18.9th position. The 18th observation is 21, and the 19th observation is also 22. The 90th percentile is a point lying 0.9 of the way from 21 to 22 and is thus 21.9.


Example 1-2

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Quartiles( 四分位數 ) are the percentage points that break down the ordered data set into quarters. The first quartile is the 25th percentile. It is the point below which lie 1/4 of the data. The second quartile is the 50th percentile. It is the point below which lie 1/2 of the data. This is also called the median( 中位數 ). The third quartile is the 75th percentile. It is the point below which lie 3/4 of the data.

Quartiles – Special Percentiles( 特殊百分位數 ,p.10)

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The first quartile, Q1, (25th percentile) is often called the lower quartile( 下四分位數 ). The second quartile, Q2, (50th

percentile) is often called median or the middle quartile( 中四分位數 ). The third quartile, Q3, (75th percentile) is often called the upper quartile( 上四分位數 ). The interquartile range( 四分位數間距 ) is the difference between the first and the third quartiles.

Quartiles and Interquartile Range

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SortedSales Sales 9 6 6 9 12 10 10 12 13 13 15 14 16 14 14 15 14 16 16 16 17 16 16 17 24 17 21 18 22 18 18 19 19 20 18 21 20 22 17 24

First QuartileFirst Quartile

MedianMedian

Third QuartileThird Quartile

((n+1)P/100n+1)P/100

(20+1)25/100=5.25

(20+1)50/100=10.5

(20+1)75/100=15.75

13 + (.25)(1) = 13.25

16 + (.5)(0) = 16

18+ (.75)(1) = 18.75

QuartilesQuartiles

Example 1-3: Finding Quartiles

Position

(16-16)

Basic Stat.xls

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Example 1-3: Using the Template

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Example 1-3 (Continued): Using the Template

This is the lower part of the same This is the lower part of the same template from the previous slide.template from the previous slide.

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Exercise, p.11, 10 min

• 1-9(Ans ： Q1=9, Q2=11.6, Q3=15.5,

55%=12.32, 85%=16.5)

• 1-12(Ans ： median=51, Q1=30.5, Q3=194.25

IQR=163.75, 45%=42.2)

Basic Stat.xlsP %= (n+1)P / 100

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Measures of Variability( 衡量變異性 ) Range 全距 Interquartile range 四分位間距 Variance 變異數 Standard Deviation 標準差

Measures of Central Tendency( 衡量集中傾向 )Median 中位數Mode 眾數Mean 平均數

Other summary measures: 其他Skewness 偏態

Kurtosis 峰態

Summary Measures: Population Parameters Sample Statistics

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Median 中位數 Middle value when sorted in order of magnitude 50th percentile

Mode 眾數 Most frequently- occurring value

Mean 平均數 Average

1-3 Measures of Central Tendency or Location(p.11)

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Sales Sorted Sales

9 6 6 9 12 1010 1213 1315 1416 1414 1514 1616 1617 1616 1724 1721 1822 1818 1919 2018 2120 2217 24

Median

Median50th Percentile

(20+1)50/100=10.5 16 + (.5)(0) = 16

The median is the middle value of data sorted in order of magnitude. It is the 50th percentile.

Example – Median (Data is used from Example 1-2)

See slide # 19 for the template outputSee slide # 19 for the template output

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. . . . . . : . : : : . . . . .--------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24

. . . . . . : . : : : . . . . .--------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24

Mode = 16

The mode is the most frequently occurring value. It is the value with the highest frequency.

Example - Mode (Data is used from Example 1-2)


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The mean( 平均數 ) of a set of observations is their average - the sum of the observed values divided by the number of observations.

Population Mean 母體平均數 Sample Mean 樣本平均數

x

Ni

N

1

Arithmetic Mean or Average

xx

ni

n

1

n

30

xx

ni

n

1 31720

1585.

Sales 9 6 12 10 13 15 16 14 14 16 17 16 24 21 22 18 19 18 20 17

317

Example – Mean (Data is used from Example 1-2)


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. . . . . . : . : : : . . . . . --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24

. . . . . . : . : : : . . . . . --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24

Median and Mode = 16

Mean = 15.85

Example - Mode (Data is used from Example 1-2)


每一點代表一個數值

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• 例 1- 4

• 1-13 ~ 1-16 (See Textbook p.656)

• 1-17 (Ans ： mean=18.34, median=19.1)

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Range 全距Difference between maximum and minimum values

Interquartile Range 四分位數間距Difference between third and first quartile (Q3 - Q1)

Variance 變異數Average*of the squared deviations from the mean

Standard Deviation 標準差Square root of the variance

Definitions of population variance and sample variance differ slightly.

1-4 Measures of Variability or Dispersion (p.15)

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SortedSales Sales Rank 9 6 1 6 9 212 10 310 12 413 13 515 14 616 14 714 15 814 16 916 16 1017 16 1116 17 1224 17 1321 18 1422 18 1518 19 1619 20 1718 21 1820 22 1917 24 20

First Quartile

Third Quartile

Q1 = 13 + (.25)(1) = 13.25

Q3 = 18+ (.75)(1) = 18.75

Minimum

Maximum

Range Maximum - Minimum = 24 - 6 = 18

Interquartile Range

Q3 - Q1 = 18.75 - 13.25 = 5.5

Example - Range and Interquartile Range (Data is used from Example 1-2)

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( )

2

2

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Population Variance 母體變異數

sx x

n

xx

nn

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2

2

1

2

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2

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Sample Variance 樣本變異數

Variance and Standard Deviation

( )

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公式證明

n

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538 0 2657.8 17130

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Calculation of Sample Variance

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Example: Sample Variance Using the Template

Note: This is Note: This is just a just a replication replication of slide #19.of slide #19.

39


• 標準差之計算 - 例 1- 5, 1- 6 (p.20) 或例 1- 2

• 1- 18 (p.22)

• 1-19 (Ans. Range=27, 57.7386, 7.5986)

• 1-20 (Ans. Range=60, 321.3788, 17.9270)

• 1-21 (Ans. Range=1186, 110287.45,

332.09555)

Basic Stat.xls

40

Dividing data into groups or classes or intervals

Groups should be:Mutually exclusive 群間互斥

• Not overlapping - every observation is assigned to only one group

Exhaustive 完全分群• Every observation is assigned to a group

Equal-width (if possible) 等寬• First or last group may be open-ended

1-5 Group Data and the Histogram群聚數據與直方圖

41

Table with two columns 兩行 listing:Each and every group or class or interval of valuesAssociated frequency of each group

• Number of observations assigned to each group• Sum of frequencies is number of observations

– N for population– n for sample

Class midpoint 組中點 is the middle value of a group or class or interval

Relative frequency 相對頻率 is the percentage of total observations in each classSum of relative frequencies = 1

Frequency Distribution 頻率分配

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x f(x) f(x)/nSpending Class ($) Frequency (number of customers) Relative Frequency

0 to less than 100 30 0.163100 to less than 200 38 0.207200 to less than 300 50 0.272300 to less than 400 31 0.168400 to less than 500 22 0.120500 to less than 600 13 0.070

184 1.000

x f(x) f(x)/nSpending Class ($) Frequency (number of customers) Relative Frequency


184 1.000

• Example of relative frequency: 30/184 = 0.163 • Sum of relative frequencies = 1

Example 1-7: Frequency Distribution p.23

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x F(x) F(x)/nSpending Class ($) Cumulative Frequency Cumulative Relative Frequency


x F(x) F(x)/nSpending Class ($) Cumulative Frequency Cumulative Relative Frequency


The cumulative frequencycumulative frequency 累積頻率累積頻率 of each group is the sum of the frequencies of that and all preceding groups.

The cumulative frequencycumulative frequency 累積頻率累積頻率 of each group is the sum of the frequencies of that and all preceding groups.

Cumulative Frequency Distribution

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頻率分配圖練習 , 10 min

• 例 1- (p.25), 以 5 為距離

Basic Stat.xls

45

A histogram histogram is a chart made of bars of different heights. 不同高度之條狀圖Widths and locations of bars correspond to

widths and locations of data groupings 寬度與位置代表群組的資料寬度與位置

Heights of bars correspond to frequencies or relative frequencies of data groupings 高度代表頻率

Histogram 直方圖

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Frequency Histogram

Histogram Example ： 1-7

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Relative Frequency Histogram

Histogram Example

48

Skewness– Measure of asymmetry of a frequency distribution

• Skewed to left 左偏 <0• Symmetric or unskewed 對稱• Skewed to right 右偏 >0

Kurtosis– Measure of flatness or peakedness of a frequency

distribution• Platykurtic (relatively flat)• Mesokurtic (normal)• Leptokurtic (relatively peaked) * 公示如 p.27

1-6 Skewness 偏度 and Kurtosis 峰度 p.25

49

Skewed to left

Skewness偏度值 -, 越左偏

50

Skewness

Symmetric

51

SkewnessSkewed to right

偏度值 +, 越右偏

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Kurtosis

Platykurtic 平扁 - flat distribution

扁度值越小 , 越平扁

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KurtosisMesokurtic - not too flat and not too peaked

54

Kurtosis

Leptokurtic 尖扁 - peaked distribution

扁度值越大 , 越尖突

55

Chebyshev’s Theorem 柴比雪夫定理Applies to any distribution, regardless of shape 可應用於任何分配之數據

Places lower limits on the percentages of observations within a given number of standard deviations from the mean

Empirical Ruler 經驗法則Applies only to roughly mound-shaped and symmetric

distributions 適用山型與對稱之數據Specifies approximate percentages of observations

within a given number of standard deviations from the mean

1-7 Relations between the Mean and Standard Deviation p.27 ( 重要 )

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116

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2

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2

At least of the elements of any distribution lie within k standard deviations of the mean

At least

Lie within

Standarddeviationsof the mean

2

3

4

Chebyshev’s Theorem

2

11

k

57

For roughly mound-shaped and symmetric distributions, approximately:

68% 1 standard deviation of the mean

95% Lie within

2 standard deviations of the mean

All 3 standard deviations of the mean

Empirical Rule 經驗法則

58


• Exercise 1- 22

Basic Stat.xls

59

Pie Charts 圓餅圖Categories represented as percentages of total

Bar Graphs 直條圖Heights of rectangles represent group frequencies

Frequency Polygons 頻率圖 Height of line represents frequency

Ogives 累加頻率圖 Height of line represents cumulative frequency

Time Plots 時間圖Represents values over time

1-8 Methods of Displaying Data

60

Pie Chart

61

Bar Chart

Average Revenues

Average Expenses

Fig. 1-11 Airline Operating Expenses and Revenues

1 2

1 0

8

6

4

2

0

A i r li n e

American Continental Delta Northwest Southwest United USAir

62

Relative Frequency Polygon Ogive

Frequency Polygon and Ogive

50403020100

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0.2

0.1

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63

OSAJJMAMFJDNOSAJJMAMFJDNOSAJJMAMFJ

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Month

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ions

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ons

M o nthly S te e l P ro d uc tio n

(P ro b le m 1 -4 6 )

Time Plot

64

圖形練習 , 10 min

• 1- 24

• 1- 25

1-24.xls 1-25.xls

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Stem-and-Leaf Displays 莖葉 Quick-and-dirty listing of all observations 快速瀏覽所有觀測值 Conveys some of the same information as a histogram 將資料轉

化成直方圖 Box Plots 盒形圖

Median Lower and upper quartiles Maximum and minimum

Techniques to determine relationships 關係 and trends 趨勢 , identify outliers 離群值 and influential 有影響的 observations, and quickly describe 快速描述 or summarize 總結 data sets.

Techniques to determine relationships 關係 and trends 趨勢 , identify outliers 離群值 and influential 有影響的 observations, and quickly describe 快速描述 or summarize 總結 data sets.

1-9 Exploratory Data Analysis – EDA探索性資料分析

66

1 122355567 (10 ~) 2 0111222346777899 (20 ~) 3 012457 (30 ~) 4 11257 (40 ~) 5 0236 (50 ~) 6 02 (60 ~)

1 122355567 (10 ~) 2 0111222346777899 (20 ~) 3 012457 (30 ~) 4 11257 (40 ~) 5 0236 (50 ~) 6 02 (60 ~)

Example 1-8: Stem-and-Leaf Display

67

X X *o

MedianQ1 Q3InnerFence

InnerFence

OuterFence

OuterFence

Interquartile Range

Smallest data point not below inner fence

Largest data point not exceeding inner fence

Suspected outlierOutlier

Q1-3(IQR)Q1-1.5(IQR) Q3+1.5(IQR)

Q3+3(IQR)

Elements of a Box PlotElements of a Box Plot

Box Plot 盒形圖

離群值

IQR

一半數據在盒內

68

Example: Box Plot

69


• 1- 27

BoxPlot.xls

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1-10 Using the Computer – The Template Output

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Using the Computer – Template Output for the Histogram

72

Using the Computer – Template Output for Histograms for Grouped Data

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Using the Computer – Template Output for Frequency Polygons & the Ogive for Grouped Data

74

Using the Computer – Template Output for Two Frequency Polygons for Grouped Data

75

Using the Computer – Pie Chart Template Output

76

Using the Computer – Bar Chart Template Output

77

Using the Computer – Box Plot Template Output

78

Using the Computer – Box Plot Template to Compare Two Data Sets

79

Using the Computer – Time Plot

Template

80

Using the Computer – Time Plot

Comparison Template

1 complete business statistics by amir d. aczel & jayavel sounderpandian 7 th edition. prepared...

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