section 1.1 statistics is the science of conducting studies to collect, organize, summarize, analyze...

Section 1.1Section 1.1StatisticsStatistics

Is the science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data.

Statistics :Statistics :

Descriptive & Inferential Descriptive & Inferential StatisticsStatistics

consists of the collection, organization, summarization and presentation of data.

Descriptive Statistics :Descriptive Statistics :

consists of generalizing from samples to population, performing estimation and hypothesis tests, determining relationships among variable, and making predictions.

Inferential Statistics :Inferential Statistics :

consists of all subjects (human or otherwise) that are being studied.

Population :Population :

is a group of subjects selected from population.

Sample :Sample :Population

Sample

Read the following and answer the questionsRead the following and answer the questions: :

A study conducted at a Community College revealed that students who attended class 95 to 100% of the time usually received an A in the class. Students who attended class 80 – 90% of the time usually received a B or C in the class. Students who attended less than 80% of the time usually received a D or an F or eventually withdrew from the class.

Based on this information, attendance and grades are related. The more you attend class, the more likely you will receive a higher grade.

Attendance and GradesAttendance and Grades

The variable are grades and attendance.

1. What are the variables under study?1. What are the variables under study?

The data is consist of specific grades and attendance number.

2. What are the data in the study?2. What are the data in the study?

These are descriptive statistic.

3. Are descriptive, inferential, or both types of 3. Are descriptive, inferential, or both types of statistics used?statistics used?

The population under study is students at

a community college .

4. What is the population under study?4. What is the population under study?

While not specified, we probably have data from a sample of a community college students.

5. Was a sample collected? If so, from where?5. Was a sample collected? If so, from where?

Based on the data, it appears that in general, the better you attendance the higher your grade.

6. From the information given, comment on the 6. From the information given, comment on the relationship between the variables.relationship between the variables.

Section 1.2Section 1.2Variable and Types of DataVariable and Types of Data

Is a characteristic or attribute that can assume different values.

Variable :Variable :

The classification of variables can be The classification of variables can be summarized as follow:summarized as follow:

Data

QuantitativeQualitative

ContinuousDiscrete

Classification of VariablesQualitative Variable: are variables that can be placed into distinct categories, according to some characteristics or attributes.

Example:

If subjects are classified according to gender(male or female), then the variable here is gender which is

qualitative. Other examples is geographic locations, eye color, hair color.

Quantitative Variable: are numerical and can be ordered or ranked .

Example :

The variable age is numerical, and people can be ranked according to value of their ages. Other variables like height, weight are also Quantitative variable.

Variable and Types of DataVariable and Types of Data

Assume values that can be counted.

Discrete Variable:Discrete Variable:

Can assume an infinite number of values between any two specific values. They are obtained by measuring. They often include fractions and decimals.

Continuous Variable:Continuous Variable:

Measurement level for each variableMeasurement level for each variable

classifies data into mutually exclusive (non-overlapping), exhausting categories in which no order or ranking can be imposed on the data.

1) Nominal level of measurement :1) Nominal level of measurement :

Zip code, Gender, Eye color, Political affiliation, Religious affiliation, Major field, Nationality.

- Examples:- Examples:

classifies data into categories that can be ranked; however, precise differences between the ranks do not exist.

2) Ordinal level of measurement :2) Ordinal level of measurement :

Grade (A,B,C,D,F), Judging (first place, second place), Rating scale (poor, good, excellent), Ranking of tennis player.

- Examples:- Examples:

Ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero.

3) Interval level of measurement :3) Interval level of measurement :

SAT score, IQ, Temperature.

- Examples:- Examples:

Possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist when the same variable is measured on two different members of the population.

4) Ratio level of measurement :4) Ratio level of measurement :

Height, Weight, Time, Salary, Age.

- Examples:- Examples:

Read the following information about the Read the following information about the transportation industry and answer the transportation industry and answer the

questionsquestions: :

Transportation safety

The chart shows the number of job-related injuries for each of the transportation industries for 1998 :

Industry Number of injuries

Railroad 4520

Intercity bus 5100

Subway 6850

Trucking 7144

Airline 9950

Safe TravelSafe Travel

The variable are industry and job-related injuries.

1. What are the variables under study?1. What are the variables under study?

The type of industry is a qualitative variable, while the number of job-related injuries is quantitative.

2. Categorize each variable as quantitative or 2. Categorize each variable as quantitative or qualitative.qualitative.

The number of job-related injuries is discrete.

3. Categorize each quantitative variable as discrete 3. Categorize each quantitative variable as discrete or continuous?or continuous?

Type of industry is nominal, and the number job-related injuries is ratio.

4. Identify the level of measurement for each variable.4. Identify the level of measurement for each variable.

The railroads do show fewer job-related injuries; however, there may be other things to consider. For example, railroads employ fewer people than the other transportation industries in the study.

5. The railroad is shown as the safest 5. The railroad is shown as the safest transportation industry. Does that mean railroads transportation industry. Does that mean railroads have fewer accidents than the other industries? have fewer accidents than the other industries? Explain.Explain.

A person’s choice of transportation might also be affected by convenience issue, cost, service, etc.

6. What factors other than safety influence a 6. What factors other than safety influence a person’s choice of transportation?person’s choice of transportation?

Answers will vary. One possible answer is that the railroads have the fewest job-related injuries, while the airline industry has the most job-related injuries (more than twice those of railroad industry). The numbers of job-related injuries in the subway and trucking are fairly comparable.

7. From the information given, comment on the 7. From the information given, comment on the relationship between variables.relationship between variables.

This method allowed me to make sure that I had representation from each area of the united state.

6. Why was the method more appropriate for this type of 6. Why was the method more appropriate for this type of data collection?data collection?

Convenience samples may not be representative of the population, and convenience sample of adolescents would probably differ greatly from the general population with regard to the influence of American culture on illegal drug use.

7. If a convenience sample were obtained, consisting of 7. If a convenience sample were obtained, consisting of only adolescence, how would the results of the study only adolescence, how would the results of the study be affected?be affected?

Exercises Page 26

Q 7, 8, 9 , 10