Statistics Ⅰ

• Teacher ：刘 伟 公共经济管理学院 统计系• E-mail ： limitzifeng@163.com

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Chapter 1 Data and Statistics

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Applications in Business and Economics

Data

Data Sources

Descriptive Statistics

Statistical Inference

Computers and Statistical Analysis

Applications in Business and Economics

Public accounting firms use statisticalsampling procedures when conductingaudits for their clients.

Financial advisors use price-earnings ratios anddividend yields to guide their investmentrecommendations.

Finance （财务）

Accounting （会计）

Applications in Business and Economics

A variety of statistical quality control charts are used to monitorthe output of a production process.

Production （生产）

Electronic point-of-sale scanners atretail checkout counters are used tocollect data for a variety of marketingresearch applications.

Marketing （市场营销）

Applications in Business and Economics

Economics （经济）Economists use statistical informationin making forecasts about the future ofthe economy or some aspect of it.

Data and Data Sets• Data （数据） are the facts and figures collected, summarized, analyzed, and interpreted.

The data collected in a particular study are referred to as the data set. （数据集）

The elements are the entities on which data are collected.

A variable is a characteristic of interest for the elements.

The set of measurements collected for a particular element is called an observation.

The total number of data values in a data set is the number of elements multiplied by the number of variables.

Elements （个体） , Variables （变量） , and Observations （观察值）

Stock Annual Earn/Exchange Sales ($M) Share($)

Data, Data Sets, Elements, Variables, and

Observations

Company

Dataram EnergySouth Keystone LandCare Psychemedics

AMEX 73.10 0.86 OTC 74.00 1.67 NYSE 365.70 0.86 NYSE 111.40 0.33 AMEX 17.60 0.13

VariablesEleme

nt

Names

Data Set

Observation

Scales of Measurement 测量尺度

The scale indicates the data summarization and statistical analyses that are most appropriate. The scale indicates the data summarization and statistical analyses that are most appropriate.

The scale determines the amount of information contained in the data. The scale determines the amount of information contained in the data.

Scales of measurement include: Scales of measurement include:Nominal （名义尺度）Ordinal （顺序尺度）

Interval （间隔尺度）

Ratio （比率尺度）

Scales of Measurement• NominalNominal

A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may be used.

Data are labels or names used to identify an attribute of the element. Data are labels or names used to identify an attribute of the element.

Example: Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on.

Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on).

Example: Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on.

Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on).

Scales of Measurement

Nominal

Scales of Measurement• Ordinal

A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may be used.

The data have the properties of nominal data and the order or rank of the data is meaningful. The data have the properties of nominal data and the order or rank of the data is meaningful.

Scales of Measurement

• Ordinal

Example: Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.

Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).

Example: Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.

Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).

Scales of Measurement

• Interval

Interval data are always numeric. Interval data are always numeric.

The data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure.

The data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure.

Scales of Measurement

• Interval

Example: Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 points more than Kevin.

Example: Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 points more than Kevin.

Scales of Measurement• Ratio

The data have all the properties of interval data and the ratio of two values is meaningful. The data have all the properties of interval data and the ratio of two values is meaningful.

Variables such as distance, height, weight, and time use the ratio scale. Variables such as distance, height, weight, and time use the ratio scale.

This scale must contain a zero value that indicates that nothing exists for the variable at the zero point. This scale must contain a zero value that indicates that nothing exists for the variable at the zero point.

Scales of Measurement

• Ratio

Example: Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.

Example: Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.

Compare

Practice:Indicate measurement scale of each of the following variables• Annual sales• Soft-drink size (small, medium, large)• Employee classification ( GS1 to GS8) • Earnings per share• Method of payment (cash, check, credit

card )

ratio, ordinal, ordinal, ratio, nominal

Data can be further classified as being qualitative or quantitative. Data can be further classified as being qualitative or quantitative.

The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.

The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.

In general, there are more alternatives for statistical analysis when the data are quantitative. In general, there are more alternatives for statistical analysis when the data are quantitative.

Qualitative and Quantitative Data

Qualitative Data Labels or names used to identify an attribute of each element Labels or names used to identify an attribute of each element

Often referred to as categorical data Often referred to as categorical data

Use either the nominal or ordinal scale of measurement Use either the nominal or ordinal scale of measurement

Can be either numeric or nonnumeric Can be either numeric or nonnumeric

Appropriate statistical analyses are rather limited Appropriate statistical analyses are rather limited

Quantitative Data

Quantitative data indicate how many or how much: Quantitative data indicate how many or how much:

discrete, if measuring how many discrete, if measuring how many

continuous, if measuring how much continuous, if measuring how much

Quantitative data are always numeric. Quantitative data are always numeric.

Ordinary arithmetic operations are meaningful for quantitative data. Ordinary arithmetic operations are meaningful for quantitative data.

Practice:State whether each of the following variablesis qualitative or quantitative? • Annual sales• Soft-drink size (small, medium, large)• Employee classification ( GS1 to GS8) • Earnings per share• Method of payment (cash, check, credit

card )

quantitative, qualitative, qualitative, quantitative, qualitative, qualitative, quantitative, qualitative, qualitative

Scales of Measurement

Qualitative

Qualitative

Quantitative

Quantitative

Numerical

Numerical

Numerical

Numerical

Non-numerical

Non-numerical

DataData

NominalNominal OrdinalOrdinal NominalNominal OrdinalOrdinal IntervalInterval RatioRatio

Cross-Sectional Data( 截面数据 )

Cross-sectional data are collected at the same or approximately the same point in time. Cross-sectional data are collected at the same or approximately the same point in time.

Example: data detailing the number of building permits issued in June 2003 in each of the counties of OhioTable 1.1 on page 5.

Example: data detailing the number of building permits issued in June 2003 in each of the counties of OhioTable 1.1 on page 5.

Time Series Data

Time series data are collected over several time periods. Time series data are collected over several time periods.

Example: data detailing the number of building permits issued in Lucas County, Ohio in each of the last 36 months

Example: data detailing the number of building permits issued in Lucas County, Ohio in each of the last 36 months

Practice: Page 20 : excise 13a. Quantitative - Earnings measured in billions of dollars

b. Time series with 6 observations c. Volkswagen's annual earnings.

d. Time series shows an increase in earnings. An increase would be expected in 2003, but it appears that the rate of increase is slowing.

Data Sources

• Existing Sources Existing Sources

Within a firm – almost any department

Business database services – Dow Jones & Co.

Government agencies - U.S. Department of Labor

Industry associations – Travel Industry Association of America

Special-interest organizations – Graduate Management Admission Council

Internet – more and more firms

• Statistical StudiesStatistical Studies

Data Sources

In experimental studies the variables of interestare first identified. Then one or more factors arecontrolled so that data can be obtained about howthe factors influence the variables.

In experimental studies the variables of interestare first identified. Then one or more factors arecontrolled so that data can be obtained about howthe factors influence the variables.

In observational (non-experimental) studies no attempt is made to control or influence the variables of interest.

In observational (non-experimental) studies no attempt is made to control or influence the variables of interest.

a survey is a

good example

Data Acquisition ConsiderationsTime Requirement

Cost of Acquisition

Data Errors

• Searching for information can be time consuming.• Information may no longer be useful by the time it is available.

• Organizations often charge for information even when it is not their primary business activity.

• Using any data that happens to be available or that were acquired with little care can lead to poor and misleading information.

Descriptive Statistics

• Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.– Tabular– Graphical– Numerical

Example: Hudson Auto Repair

The manager of Hudson Autowould like to have a betterunderstanding of the costof parts used in the enginetune-ups performed in theshop. She examines 50customer invoices for tune-ups. The costs

of parts,rounded to the nearest dollar, are listed on

the nextslide.

91 78 93 57 75 52 99 80 97 62

71 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 109

85 97 88 68 83 68 71 69 67 74

62 82 98 101 79 105 79 69 62 73

91 78 93 57 75 52 99 80 97 62

71 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 109

85 97 88 68 83 68 71 69 67 74

62 82 98 101 79 105 79 69 62 73

Example: Hudson Auto Repair

Sample of Parts Cost for 50 Tune-ups

Tabular Summary: Frequency and Percent Frequency

50-59 60-69 70-79 80-89 90-99 100-109

2 13 16 7 7 5 50

4 26 32 14 14 10 100

(2/50)100

Parts Cost ($)

Parts Frequency

PercentFrequency

Graphical Summary: Histogram

2222

4444

6666

8888

10101010

12121212

14141414

16161616

18181818

PartsPartsCost ($)Cost ($) PartsPartsCost ($)Cost ($)

Freq

uen

cyFr

eq

uen

cyFr

eq

uen

cyFr

eq

uen

cy

505059 6059 6069 7069 7079 79 808089 9089 9099 100-11099 100-110505059 6059 6069 7069 7079 79 808089 9089 9099 100-11099 100-110

Tune-up Parts Cost

Numerical Descriptive Statistics

Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50).

The most common numerical descriptive statistic is the average (or mean).

Statistical Inference

Population

Sample

Statistical inference

Census

Sample survey

the set of all elements of interest in a particular study

a subset of the population

the process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population

collecting data for a population

collecting data for a sample

Process of Statistical Inference

1. Population consists of all

tune-ups. Averagecost of parts is

unknown.

2. A sample of 50engine tune-ups

is examined.

3. The sample data provide a sample

average parts costof $79 per tune-up.

4. The sample averageis used to estimate the population average.

Practice: Page 20, excise 15• a. All subscribers of Business Week in North

America at the time the survey was conducted. • b. Quantitative • c. Qualitative ( yes or no) • d. Cross-sectional - all the data relate to the

same time. • e. Using the sample results, we could infer or

estimate 59% of the population of subscribers have an annual income of $75,000 or more and 50% of the population of subscribers have an American Express credit card.

Computers and Statistical Analysis

Statistical analysis often involves working with large amounts of data. Computer software is typically used to conduct the analysis. Statistical software packages such as Microsoft Excel and Minitab are capable of data management, analysis, and presentation.

Instructions for using Excel and Minitab are provided in chapter appendices.

End of Chapter 1