001 lesson 1 statistical techniques for business & economics

IBS Statistics Year 1Dr. Ning DING

[email protected], Friday & Monday

mailto:[email protected]

Table of content• Chapter 1: What is statistics?

– Why study statistics?– What is meant by statistics?– Types of statistics– Types of variables– Levels of measurement

• Norminal-Level Data• Ordinal-Level Data• Interval-Level Data

– Ethics and Statistics

• Chapter 2: Describing data– Frequency tables– Frequency distributions– Graphic presentation

Learning Goals• Chapter 1: What is statistics?

– Understand why we study statistics– Explain what is meant by descriptive and inferential statistics– Distinguish between a qualitative and quantitative variable– Describe how a discrete variable is different from a continous variable– Distinguish among the nominal, ordinal, interval and ratio levels of measurement

• Chapter 2: Describing data– Organize qualitative data into a frequency table– Present a frequency table as a bar chart or a pie chart– Organize quantitative data into a freqency distribution– Present a frequency distribution for quantitative data using histograms, frequency polygons, and cumulative

frequency polygons.

1. IntroductionChapter 1: What is Statistics?

Statistics are everywhere.


Statistics help you make decisions.


Statistics give you a better understanding.


1. Adequate information? Additional information?

2. No misleading information?

3. Summarize the information.

4. Analyze available information.

5. Conclusions!


Statistics:

The science of collecting, organizing, presenting, analyzing and interpreting data to assist in making more effective decisions.

1. Introduction

Collect data

Chapter 1: What is Statistics?

Interpret data

Analyze data

Organize data

Present data

Making decisionsMaking decisions

2. Types of StatisticsChapter 1: What is Statistics?

Descriptive Statistics:

Methods of organizing, summarizing and presenting data in an informative way.

Inferential Statistics:

Methods used to estimate a property of a population on the basis of a sample.


Descriptive Statistics:

Inferential Statistics:


Population:

The entire set of individual or objects of interest or the measurements obtained from all individuals or objects of interest.

Sample:

A portion, or part, of the population of interest.


Population:

Sample:

Play

http://mips.stanford.edu/courses/stats_data_analsys/lesson_1/234_0_a.html

3. Types of VariablesChapter 1: What is Statistics?

Qualitative:

nonnumeric, attribute

Quantitative:

numerical


Qualitative:Qualitative:

Quantitative: Quantitative:


Discrete counting or Continuous measuring

4. Levels of MeasurementChapter 1: What is Statistics?

Nominal: •Data categories are represented by labels or names.•Even when the labels are numerically coded, the data categories have no logical order.

•Example:•Eye colour, gender, religious affiliation

Ordinal: •Data classifications are represented by sets of labels or names (high, medium, low) that have relative values.•Because of the relative values, the data classified can be ranked or ordered.

•Example:•During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.


Nominal: Nominal: Ordinal: Ordinal:

No logical order Ranked or ordered


Interval: •Similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. •There is no natural zero point.

•Example:•Temperature on the Fahrenheit scale.

Ratio: •The interval level with an inherent zero starting point. •Differences and ratios are meaningful for this level of measurement.

•Examples:•Monthly income; distance travelled by manufacturer’s representatives per month.


Interval: Interval:

Ratio: Ratio:

Ordered, Equal differences

Zero

Nominal: Nominal:

Ordinal: Ordinal:

Online Animation

http://faculty.mc3.edu/rhofman/flash03/Nov19/menulevels.html


11

Summary of the Characteristics for Levels of Measurement

Exercises 1-aChapter 1: What is Statistics?

For each of the following, determine whether the group is a sample or a population.

•The participants in a study of a new cholesterol drug.

•The drivers who received a speeding ticket Kansas City last month.

•Those on welfare in Cook County (Chicago), Illinois.

•The 30 stocks reported as a part of the Dow Jones Industrial Average.

SampleSample

SampleSample

PopulationPopulation

PopulationPopulation

P14. N.4 Ch.1

Exercises 1-bChapter 1: What is Statistics?

Refer to the Real Estate data at the back of the text, which report information on homes sold in the Denver, Colorado, area last year. Consider the following variables: selling price, number of bedrooms, township, and distance from the center of the city.

•Which of the variables are qualitative and which are quantitative?

•Determin the level of measurement for each of the variables.

P18. N.16 Ch.1

townshiptownship

Township = nominal levelTownship = nominal level

all the rest…all the rest…

All the rest…=ratioAll the rest…=ratio

2.1 Frequency TableChapter 2: Describing data

Frequency Table: •A grouping of qualitative data into mutually exclusive classes showing the number of observations in each class.

Example: Ice cream 20 vendors

Choco 6 7 5 7 7 8 7 6 9 7 Vanilla 4 10 6 8 8 9 5 6 4 8

2.1 Frequency TableChapter 2: Describing data

Relative Class Frequencies: •Show the fraction of the total number of observations in each class

Choco 6 7 5 7 7 8 7 6 9 7 Vanilla 4 10 6 8 8 9 5 6 4 8


Exercises 2-aChapter 1: What is Statistics?

A total of 1,000 residents in Minnesota were asked which season they preferred. The results were 100 liked winter best, 300 liked spring, 400 liked summer, and 200 liked fall. If the data were summarized in a frequency table, how many classes would be used? What would be the relative frequencies for each class?

P27. N.3 .Ch.2

2.2 Graphic Presentation of Qualitative Data

Chapter 2: Describing data

Bar Chart: •The classes are reported on the horizontal axis•The class frequencies on the vertical axis•The class frequencies are proportional to the heights of the bars.

Example: Ice cream 20 vendors Ice Cream Sales

Vanilla, 68Choco, 69

50

55

60

65

70

Choco Vanilla

Types

Axi

s Choco

Vanilla


Pie Chart: •Shows the proportion or percent that each class represents of the total number of frequencies


2.2 Graphic Presentation of Qualitative Data


Frequency Distribution:

2. Frequency Distribution

•A grouping of data into mutually exclusive classes showing the number of observations in each class.


Frequency Distribution: •A grouping of data into mutually exclusive classes showing the number of observations in each class.




Step 2: Class Interval

Step 3: Choose nice “round” boundaries

Step 4: Try to avoid empty and open classes

Step 1: Just enough recipe 2 to the k rule2 to the k rule

N=27 number of class=5

(55-14)/5 ≈ 8

10 -< 20 420 -< 30 130 -< 40 1040 -< 50 950 -< 60 3

N=27Practice

Exercises 2-b

A set of data consists of 45 observations between $0 and $29. What size would you recommend for the class interval?

P33. N.8 .Ch.2

25 = 32, 26 = 64, suggests 6 classes


Use interval of 5

i = 5> $30 - $06

Exercises 2-b

The Quick Change Oil Company has a number of outlets in the metropolitan Seattle area. The daily number of oil changes at the Oak Street outlet in the past 20 days are:

P34. N.12.Ch.2

a. 24 = 16, 25 = 32, suggests 5 classes


65 98 55 62 79 59 51 90 72 5670 62 66 80 94 79 63 73 71 85

b. Use interval of 10

i > ≈ 999 - 51

5

a. How many classes would you recommend?

b. What class interval would you suggest?

Exercises 2-b

The Quick Change Oil Company has a number of outlets in the metropolitan Seattle area. The daily number of oil changes at the Oak Street outlet in the past 20 days are:

P34. N.12.Ch.2


65 98 55 62 79 59 51 90 72 5670 62 66 80 94 79 63 73 71 85

c. 50

c. What lower limit would you recommend for the first class?


3. Graphic Presentation

Histogram•The classes are marked on the horizontal axis•The class frequencies on the vertical axis•The class frequencies are represented by the heights of the bars and the bars are adjacent to each other.

Polygon: •The shape of a distribution•Similar to a histogram


Example:


HistogramHistogram


Example:


PolygonPolygon

Not floating in the air



Cumulative frequency distribution:used to determine how many or what proportion of the data values are below or above a certain value.

Not floating in the air

Summary• Chapter 1: What is statistics?

– Understand why we study statistics– Explain what is meant by descriptive and inferential statistics– Distinguish between a qualitative and quantitative variable– Describe how a discrete variable is different from a continous

variable– Distinguish among the nominal, ordinal, interval and ratio

levels of measurement

• Chapter 2: Describing data– Organize qualitative data into a frequency table– Present a frequency table as a bar chart or a pie chart– Organize quantitative data into a freqency distribution– Present a frequency distribution for quantitative data using

histograms, frequency polygons, and cumulative frequency polygons.


What is the level of measurement for each of the following variables?

• A. student IQ ratings • B. distance students travel to class• C. student scores on the first statistics test• D. a classification of students by state of birth• E. a ranking of students as freshmen, sophomore, junior, and

senior• F. Number of hours students study per week

Exercises 1-a

IntervalInterval

RatioRatio

IntervalInterval

NominalNominal

OrdinalOrdinal

RatioRatio


Exercises 1-b

Place these variables in the following classification tables.

Qualitative

Quantitative

a. Salaryb. Genderc. Sales

volumen of MP3 players

d. Soft drink preference

e. Temperaturef. SAT scoresg. Student rank

in classh. Rating of a

finance professor

i. Number of home computers

Discrete Continuous

b. Genderb. Gender d. Soft drink preferenced. Soft drink preference

f. SAT scoresf. SAT scores

g. Student rank in classg. Student rank in class

h. Rating of a finance professorh. Rating of a finance professor

a. Salary a. Salary

c. Sales volume of MP3 playersc. Sales volume of MP3 players

e. Temperaturee. Temperature

i. Number of home computersi. Number of home computers


P16. N.9 Ch.1

Exercises 1-c

Place these variables in the following classification tables.

Nominal

Ordinal

a. Salaryb. Genderc. Sales

volumen of MP3 players

d. Soft drink preference

e. Temperaturef. SAT scoresg. Student rank

in classh. Rating of a

finance professor

i. Number of home computers

Discrete Continuous

b. Genderb. Gender

d. Soft drink preferenced. Soft drink preference

f. SAT scoresf. SAT scores

g. Student rank in classg. Student rank in class h. Rating of a finance professorh. Rating of a finance professor

a. Salary a. Salary

c. Sales volume of MP3 playersc. Sales volume of MP3 players

e. Temperaturee. Temperature

i. Number of home computersi. Number of home computers

Interval

Ratio


Exercises 1-dChapter 1: What is Statistics?

The table below reports the number of cars and light trucks sold by the Big Three automobile manufacturers for June 2004 and June 2005.

1. Compare the total sales in the two months. What do you conclude? Has there been an increase in sales?

P17. N.13 Ch.1



1. Compare the total sales in the two months. What do you conclude? Has there been an increase in sales?

Total sales increased 189,901 units or 21.9%.

(1,056,144-866,243)866,243



2. Compare the percent of the Big Three market for each company. Did the market increase or did GM steal sales from the other companies? Cite evidence.



2. Compare the percent of the Big Three market for each company. Did the market increase or did GM steal sales from the other companies? Cite evidence.

GM increased the market share by 9 percentage points from 43% to 52%. Crysler lost 3% and Ford lost 6%. All three companies increased the nubmer of units sold.

001 lesson 1 statistical techniques for business & economics

Education

statistics chapter

introduction statistics

study statistics

ibs statistics year

qualitative data

data values

data categories

presenting data