Lesson01

IBS Statistics Year 1

Dr. Ning DING [email protected]

What we are going to learn?

1. Why they failed in STA1?

2. Chapter 1: What is statistics?1. Why? What?

2. Types of statistics, variables

3. Levels of measurement

3. Chapter 2: Describing data1. Frequency tables

2. Frequency distributions

3. Graphic presentation

2. Chapter 1: What

is Statistics?

A. Why? What?B. Types of

statistics, variables

C. Levels of measurement

1. Why Failed in Statistics?

3. Chapter 2: Describing Data

A. Frequency tables

B. Frequency distributions

C. Graphic presentation

Summary of the reasons

Absent for the lessons;

Didn’t do the home assignments;

Ignore the EXCEL lessons;

Cannot use the theories flexibly;

Keep misconceptions and misunderstanding till the exam;

Overestimate self and underestimate the subject.

2. Chapter 1: What

is Statistics?






A. Frequency tables



Statistics are everywhere.CPP

BPP

BRM

2. Chapter 1: What

is Statistics?






A. Frequency tables



Statistics help you make decisions.

2. Chapter 1: What

is Statistics?






A. Frequency tables




Collect data

Interpret data

Analyze data

Organize data

Present data

Making decisionsMaking decisions

2. Chapter 1: What

is Statistics?






A. Frequency tables




Statistics:

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

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.

2. Chapter 1: What

is Statistics?






A. Frequency tables




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.

2. Chapter 1: What

is Statistics?






A. Frequency tables




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.

2. Chapter 1: What

is Statistics?






A. Frequency tables



Types of variables

Qualitative:

nonnumeric, attribute

Quantitative:

numerical

2. Chapter 1: What

is Statistics?






A. Frequency tables



Types of variables

Qualitative Quantitative

2. Chapter 1: What

is Statistics?






A. Frequency tables



Types of variables

Discrete counting

Continuous measuring

Salary Class Size

HeightDiscrete ContinuousDiscrete Continuous

2. Chapter 1: What

is Statistics?






A. Frequency tables



Levels of Measurement

Nominal: • Data categories are represented by labels or

names.• Even when the labels are numerically coded, the

data categories have no logical order.

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.

2. Chapter 1: What

is Statistics?






A. Frequency tables




Nominal: No logical order

Ranked or ordered

Ordinal:

2. Chapter 1: What

is Statistics?






A. Frequency tables




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.

Ratio: • The interval level with an inherent zero starting

point. • Differences and ratios are meaningful for this

level of measurement.

2. Chapter 1: What

is Statistics?






A. Frequency tables




Interval: Ratio:

IQTemperatureDistance

Interval: Ratio:

Salary

2. Chapter 1: What

is Statistics?






A. Frequency tables




2. Chapter 1: What

is Statistics?






A. Frequency tables




11

Summary of the Characteristics for Levels of Measurement

2. Chapter 1: What

is Statistics?






A. Frequency tables



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-a

2. Chapter 1: What

is Statistics?






A. Frequency tables



Exercises 1-b

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. Chapter 1: What

is Statistics?






A. Frequency tables



Frequency Table: • A grouping of qualitative data into mutually exclusive

classes showing the number of observations in each class.

2. Chapter 1: What

is Statistics?






A. Frequency tables



Relative Frequency

Total 12

5/12 = 41.67%

3/12=25.00%

4/12=33.33%

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

each class

2. Chapter 1: What

is Statistics?






A. Frequency tables



Exercises 2-aA 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. Chapter 1: What

is Statistics?






A. Frequency tables



Relative Frequency

Total 12

5/12 = 41.67%

3/12=25.00%

4/12=33.33%

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.

Graphic Presentation of Qualitative data

2. Chapter 1: What

is Statistics?






A. Frequency tables



Relative Frequency

Total 12

5/12 = 41.67%

3/12=25.00%

4/12=33.33%

Pie Chart: • Shows the proportion or percent that each class

represents of the total number of frequencies


2. Chapter 1: What

is Statistics?






A. Frequency tables



Pie charts require that you include all the categories that make up a whole. Use them only when you want to emphasize each category's relation to the whole.


2. Chapter 1: What

is Statistics?






A. Frequency tables



Frequency Distribution: • A grouping of data into mutually exclusive classes

showing the number of observations in each class.

2. Chapter 1: What

is Statistics?






A. Frequency tables



Frequency Distribution: • A grouping of data into mutually exclusive classes

showing the number of observations in each class.

2. Chapter 1: What

is Statistics?






A. Frequency tables



Frequency Distribution:

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=27

22=4 23=8 24=16

25=32 26=64 27=128

2. Chapter 1: What

is Statistics?






A. Frequency tables



Exercises 2-bA 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

2. Chapter 1: What

is Statistics?






A. Frequency tables



Exercises 2-bThe 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?

2. Chapter 1: What

is Statistics?






A. Frequency tables



Exercises 2-bThe 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?

2. Chapter 1: What

is Statistics?






A. Frequency tables



Graphic Presentation of Quantitative data

a) 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.

2. Chapter 1: What

is Statistics?






A. Frequency tables




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

Not floating in the air

2. Chapter 1: What

is Statistics?






A. Frequency tables




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


2. Chapter 1: What

is Statistics?






A. Frequency tables



Why Failed in Statistics?Why Failed in Statistics?

2. Chapter 1: What

is Statistics?






A. Frequency tables




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


2. Chapter 1: What is Statistics?

A. Why? What?B. Types of statistics, variablesC. Levels of measurement

1. Why they failed in Statistics?

3. Chapter 2: Describing DataA. Frequency tablesB. Frequency distributionsC. Graphic presentation

What we have learnt?

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-bPlace 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-cPlace 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-dThe 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

Total sales increased 189,901 units or 21.9%.

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

Exercises 1-dThe table below reports the number of cars and light trucks sold by the Big Three automobile manufacturers for June 2004 and June 2005.

P17. N.13 Ch.1

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.

Example: Dr. Tillman is Dean of the School of Business Socastee University. He wishes to prepare a report showing the number of hours per week students spend studying. He selects a random sample of 30 students and determines the number of hours each student studied last week.


15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.

Select the smallest number (k) for the number of classes such that 2k is greater than the number of observations (n).

Frequency Distribution


15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.

• If sample size (n) = 80• 21=2; 22=4; 23=8; 24=16; 25=32;

26=64; 27=128; …• The rule suggest 7 classes.

• If sample size (n) = 1000• 21=2; 22=4; 23=8; 24=16; 25=32;

26=64; 27=128; 28=256; 29=512; 210=1024 …

• The rule suggest 10 classes.

Sample size (n) = 3021=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=128; …The rule suggest 5 classes.


15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.

• The classes all taken together must cover at least the distance from the lowest value in the raw data to the highest value.

• The classes must be mutually exclusive and exhaustive.

Class interval

(next unit of Highest value – lowest value) / number of classes.

k

LHi

Usually we will chose some convenient number as class interval that satisfy the inequality.



15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.



• Highest value = 33.9 hours• Lowest value = 10.3 hours• k=5.• Hence, class interval ≥ (33.9-10.3)/5 ≈ 4.7• We choose class interval to be 5, some convenient number.

15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.


Step 3: Individual class limits

• Next unit of Highest value = 33.9 hours.• Lowest value = 10.3 hours.• Range = nu of highest – lowest = 23.5.• K=5; Interval = 5.

• With k=5 and interval = 5, the classes will cover a range of 25. • Let’s split the surplus in the lower and upper tail equally. (25-23.5)/2

= 0.75. Hence, the lower limit of the first class should be around (10.3 – 0.75)=9.55 and upper limit of the last class should be (33.8 + 0.75)=34.55.

• 9.55 and 34.55 look odd. Some convenient and close numbers would be 10 and 35.

Hours studying Frequency, f

10 up to 15

15 up to 20

20 up to 25

25 up to 30

30 up to 35

“10 up to 15” means the interval from 10 to 15 that includes 10 but not 15.

Example:

Step 4: Tally the data

10 up to 15

Hours studying

15 up to 20

20 up to 25

25 up to 30

30 up to 35

7

12

7

3

1

15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.


15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.

Step 5: Count the number

Hours studying Frequency, f

10 up to 15 7

15 up to 20 12

20 up to 25 7

25 up to 30 3

30 up to 35 1


Frequency Distribution15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.

Step 5: Count the number

Hours f Relative Frequency

10 up to 15 7 7/30=.233 15 up to 20 12 12/30=.400

20 up to 25 7 7/30=.233

25 up to 30 3 3/30=.100

30 up to 35 1 1/30=.033

TOTAL 30 30/30=1

Relative Frequency DistributionRelative Frequency Distribution

Exercises 2-bA set of data consists of 38 observations. How many classes would you recommend for the frequency distribution?

P33. N.7 .Ch.2

25 = 32, 26 = 64, therefore, 6 classes

A set of data consists of 230 observations between $235 and $567. What class interval would you recommend.

27 = 128, 28 = 256, suggests 8 classes

Class intervals of 40, 45, or 50 all would be acceptable.

Date post:	17-Nov-2014
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Lesson01

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