Lecturer: DAO MINH ANH Faculty of Business and Administration Foreign Trade University Email: [email protected].

Lecturer: DAO MINH ANH

Faculty of Business and Administration

Foreign Trade University

Email: [email protected]

Textbook Business Mathematics and Statistics – 5th

edition (A. Francis) References:- Essentials of Statistics for Business and

Economics – 3rd edition, 2003 (Anderson Sweeney Williams)

- Statistics for Business and Economics – 4th edition (Paul Newbold)

Class attendance: 10% Group Assignment and presentation: 30% Final exam: 60%

Tracking information: sales, inventory, products being transported, refunded items, customer information (demographic), business performance of suppliers, etc.

Collecting and analyzing data “Market basket”

Decision making on:- Future trend- Inventory Management- Customer Relationship Management...

I. What is statistics?II. DefinitionsIII. Descriptive statistics and Inferential

statisticsIV. Qualitative and Quantitative dataV. Scales of Measurement

- What first appear in your mind when we talk about “statistics”?

interest rates, population, stock market interest rates, population, stock market prices, unemployment…prices, unemployment…

- In a very general way:- In a very general way:

Statistics

numerical numerical informationinformation

- Furthermore:- Furthermore:

Statistics

Statistical methodsStatistical methods

- Collect

- describe

- summarize

- present

- analyze

Making sense of numerical information Dealing with uncertainty Sampling Analyzing relationships Forecasting Decision making in an uncertain

environment

In order to make the right decision or forecast, decision-makers require as much information as possible.

However, after being collected numerical information is under the raw form.

impossible to comprehend thoroughlyimpossible to comprehend thoroughly

These information need to be summarized, organized and analyzed so that important features emerges

“Statistics is the science of uncertainty” In statistics we have to deal with the

question what might be, what could be… not what is

One task of statistics is to estimate the level of uncertainty

E.g: Before bringing a new product to market, market research survey about the likely level of demand of this product maybe undertaken?

should the survey cover all potential should the survey cover all potential buyers (population)?buyers (population)?

Absolutely impossible due to the huge costs of time, money, people…

Sampling

Let’s consider some examples below:(i) Does the growth rate of money supply

influence the inflation rate?(ii) If the price of a product rise by 5%, what

is the effect on the sales of this product?

- The relationships between variables will be analyzed in a quantitative way not qualitative way based on the past behaviors of these variables

Reliable predictions play a key role in management and making decision

For example: investment decisions must be made well ahead of the time at which a new product can be brought to market;

Essentially, forecasts of future values are obtained through the information of past behaviors

The analysis of this information suggests future trend

A particular problem for management: making decisions in the condition of incomplete information

Therefore, under such circumstances, possible options should be raised and considered

AccountingPublic accounting firms use statistical sampling procedures when conducting audits for their clients.

EconomicsEconomicsEconomists use statistical Economists use statistical information in making information in making forecasts about the future of forecasts about the future of the economy or some the economy or some aspects of it.aspects of it.

MarketingElectronic point-of-sale scanners at retail checkout counters are used to collect data for a variety of marketing research applications.

ProductionProductionA variety of statistical quality A variety of statistical quality control charts are used to control charts are used to monitor the output of a monitor the output of a production process.production process.

FinanceFinancial advisors use price-earnings ratios and dividend yields to guide their investment recommendations.

1/ Variable is a characteristic that changes or varies over time for different individuals or objects under consideration

2/ Experimental Units (elements) are items or objects on which measurements are taken

4/ Population is the WHOLE set of all items or individuals of interest

5/ Sample is an observed subset of population values

Population vs. SamplePopulation vs. Sample

a b c d

ef gh i jk l m n

o p q rs t u v w

x y z

Population Sample

b c

g i n

o r u

y

Statistics

Descriptive Statistics Inferential Statistics

Descriptive statistics: Methods used to summarize and describe the main features of the whole population in quantitative term.

Tabular, graphical, and numerical methods (mean, median, variance, standard deviation…)

Used when we can enumerate the whole population

- Collect datae.g., Survey, Observation,

Experiments

n

x i

- Present data- Present datae.g., Charts and e.g., Charts and graphsgraphs

- Characterize data- Characterize datae.g., Calculate mean e.g., Calculate mean ==

Inferential statistics: Procedures used to draw conclusions or inferences about the characteristics of a population from information obtained from the sample.

Making estimates, testing hypothesis… Used when we can not enumerate the

whole population

Sample Population

Sample statistics

(known)

Population parameters

(unknown, but can be estimated from sample evidence

Inference

Estimation◦ e.g., Estimate the population

mean weight using the sample mean weight

Hypothesis Testing◦ e.g., Use sample evidence to test

the claim that the population mean weight is 120 pounds

Drawing conclusions and/or making decisions concerning a population based on sample results.

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

Depends on whether the data are qualitative or Depends on whether the data are qualitative or quantitative, we choose the most quantitative, we choose the most appropriate statistical methodsappropriate statistical methods

Depends on whether the data are qualitative or Depends on whether the data are qualitative or quantitative, we choose the most quantitative, we choose the most appropriate statistical methodsappropriate statistical methods

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

Labels or names used to identify an attribute of each element.

Often be referred to as categorical data Nominal or ordinal scale of measurement

will be applied to summarize this kind of data

Usually nonnumeric data Therefore, appropriate statistical analyses

are rather limited in comparison with those of quantitative data

Eye colors: 1.Brown 2.Black 3.Blue 4.Green Marital status: 1. Single 2. Married

3. Divorced 4. Widowed

Quantitative data can be described as data under the numeric form. It indicates how many or how much:

Quantitative data can be described as data under the numeric form. It indicates how many or how much:

There are two types of quantitative data: There are two types of quantitative data:

discrete datadiscrete data: :

- can measure can measure precisely.precisely.- Only a finite number Only a finite number of values is possible. of values is possible. - Example:Example:

Continuous dataContinuous data: :

- can not measured can not measured preciselyprecisely- An infinite number of An infinite number of values is possible. values is possible. - Example:Example:

E.g. E.g. (i)(i)The number of students in a classThe number of students in a class(ii)(ii)The number of correct answers in a The number of correct answers in a

testtest(iii)(iii)People’s height, weight; students’ GPAPeople’s height, weight; students’ GPA

Scales of measurement include: Scales of measurement include:

NominalNominal IntervalInterval

OrdinalOrdinal RatioRatio

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

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

These scales of measurement gradually develop, from the simplest form (nominal scale) to the most sophisticated one (interval/ratio scale).

Ratio/Interval Scale

Ordinal Scale

Nominal Scale

Highest Level

Complete Analysis

Higher Level

Mid-level Analysis

Lowest Level

Basic Analysis

Categorical Codes ID Numbers Category Names

Rankings

Ordered Categories

Measurements

Level of measurements

Nominal

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

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

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).

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).

Please state which fuel are you using at home?

1.Firewood2.Coal3.Oil4.Gas

Please state which fuel are you using at home?

1.Firewood2.Coal3.Oil4.Gas

Ordinal

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

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

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).

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).

Please order the kind of fuel that is the most favorite one for you?

( ) Firewood( ) Coal( ) Oil( ) Gas

Please order the kind of fuel that is the most favorite one for you?

( ) Firewood( ) Coal( ) Oil( ) Gas

Interval

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

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

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

There is noThere is no zero value zero value that indicates that indicates that nothing exists for the variable at the zero point.that nothing exists for the variable at the zero point. There is noThere is no zero value zero value that indicates that indicates that nothing exists for the variable at the zero point.that nothing exists for the variable at the zero point.

Interval

The ratio of two values of interval scale is not The ratio of two values of interval scale is not Meaningful because there is no zero value in this Meaningful because there is no zero value in this scale.scale.

The ratio of two values of interval scale is not The ratio of two values of interval scale is not Meaningful because there is no zero value in this Meaningful because there is no zero value in this scale.scale.

ExampleExample: Melissa has an SAT score of 800, : Melissa has an SAT score of 800, while Kevin has an SAT score of 400. while Kevin has an SAT score of 400. Melissa scored 400 points more than Kevin.Melissa scored 400 points more than Kevin.

Please state your opinion on customer service at one restaurant?

-3 -2 -1 +1 +2 +3

Not friendly Friendly

Please state your opinion on customer service at one restaurant?

-3 -2 -1 +1 +2 +3

Not friendly Friendly

Ratio

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

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

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

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.

Assume that you spend VND 100,000 for your family’s fuel. Please distribute this amount for different kinds that you are interested in?

1.Firewood.................VND2.Coal.........................VND3.Oil............................VND4.Gas..........................VND

Assume that you spend VND 100,000 for your family’s fuel. Please distribute this amount for different kinds that you are interested in?

1.Firewood.................VND2.Coal.........................VND3.Oil............................VND4.Gas..........................VND

Example: there is a survey on FTU’s students. Describe them as quantitative or qualitative, and the scales of measurement

1. Full name:..........................................2. Sex: Male Female3. Age :4. Which year student:

1st 2nd 3rd 4th

5. a/ Have you got a part-time job?Yes No

b/ If yes, how many hours per week?...........c/ What do you think how much does your part-time job

fit your study field?Very suitable Not at all

5 4 3 2 1

Define the issue◦ what are the purpose and objectives of the

survey?

Define the population of interest

Formulate survey questions◦ make questions clear and unambiguous

◦ use universally-accepted definitions

◦ limit the number of questions

Pre-test the survey◦ pilot test with a small group of participants

◦ assess clarity and length

Determine the sample size and sampling method

Select Sample and administer the survey

Closed-end Questions◦ Select from a short list of defined choices

Example: Major: __business__liberal arts __science __other

Open-end Questions◦ Respondents are free to respond with any

value, words, or statementExample: What did you like best about this course?

Demographic Questions◦ Questions about the respondents’ personal

characteristicsExample: Gender: __Female __ Male

A Population is the set of all items or individuals of interest◦ Examples: All likely voters in the next

election All parts produced today

All sales receipts for November

A Sample is a subset of the population◦ Examples: 1000 voters selected at random for

interviewA few parts selected for destructive testingEvery 100th receipt selected for audit

Less time consuming than a census

Less costly to administer than a census

It is possible to obtain statistical results of a sufficiently high precision based on samples.

Items of the sample are chosen based on known or calculable probabilities

Probability Samples

Simple

RandomSystematicStratified Cluster

Every individual or item from the population has an equal chance of being selected

Selection may be with replacement or without replacement

Samples can be obtained from a table of random numbers or computer random number generators

Population divided into subgroups (called strata) according to some common characteristic

Simple random sample selected from each subgroup

Samples from subgroups are combined into one

PopulationDividedinto 4strata

Sample

Decide on sample size: n Divide frame of N individuals into groups

of k individuals: k=N/n Randomly select one individual from the

1st group Select every kth individual thereafter

N = 64

n = 8

k = 8

First Group

Population is divided into several “clusters,” each representative of the population

A simple random sample of clusters is selected◦ All items in the selected clusters can be used, or

items can be chosen from a cluster using another probability sampling technique

Population divided into 16 clusters. Randomly selected

clusters for sample

There are three kinds of lies…..◦ Lies◦ Damn Lies◦ Statistics

You need to make statistics work for you, not lie for you!

THANK YOU!

Describe the variable implicit in these 10 items as quantitative or qualitative, and describe the scale of measurement

1. Age of household head2. Sex of household head3. Number of people in household4. Use of electric heating (yes/no)5. Numbers of large appliances used daily6. Average number of hours heating is on7. Average number of heating days8. Household incomes9. Average monthly electric bill10.Ranking of this electric company among 4 electricity

suppliers

You have to do a survey on vacation/ summer holiday of FTU’s students. Work with your groups to create a questionnaire for this assignment.

It should contain:- The goal of the survey- Objects- Content