Exercise 1:A national survey asked 5000 U.S. employed adults how far, in miles, they commute to work.

(a) Identify the variable.

(b) Is the variable quantitative or qualitative?

(c) What is the implied population?

Step 1:Identify the variable.

When designing a study, some of the first decisions we need to make are what to measure and who to include. A variable is the measured characteristic or feature of the included individuals.

Example:

If a study is being conducted on professional cyclists, variables might be age, weight, muscle mass, height,nationality, gender,and so on.

Instructions:

State the variableinthecommutingstudyabove.

Step 2:Determine if the variable is quantitative or qualitative.

A variable can be quantitative, meaning numerical, or qualitative, meaning categorical. Identifying if a variable is quantitative or qualitative is important for knowing which statistical methods can be used to analyze the data.

Example:

Variables like nationality and gender are qualitative. These variables do not have numerical attributes and simply place individuals in one of several categories or groups. Variables like age, height, and weight are quantitative. These variables are measured numerically.

Instructions:

Identify whether the variable of thecommutingstudy is quantitative or qualitative.

Step 3:Identify the implied population.

Collecting data from every individual of interest is often unrealistic, so samples are used. Statistics gathered from the study of a sample of individuals may be useful to describe the entire population (all of the individuals of interest).Understanding the difference between the population and the sample is crucial to properly interpret statistical results.

Example:

In a study of professional cyclists, perhaps data is collected from only 100 cyclists that are representative of all professional cyclists. In this case the population, or all individuals of interest, is the collection of all professional cyclists. The sample is the group of 100 cyclists that are included in the study.

Instructions:

Based on the description of thecommutingstudy, determine the population, or all the individuals of interest.

Exercise 2:Categorize these measurements associated with marathon running according to level: nominal, ordinal, interval, or ratio.

(a) ageof participant

(b)state or country of residency

(c)finishing time

(d)finishing position (place)

(e) year of first marathon

Step 1:Identify nominal measurements.

In addition to categorizing data or variables as quantitative or qualitative, we can categorize based on the level of measurement. This type of categorization helps us know which type of arithmetic is appropriate for the data.Nominal measurementsare categorical and are not able to be ordered.

Example:

A study is being conducted on the employees of a company.Onevariable of the study is the college or university from which the employee graduated. This variable is nominal because the colleges and universities cannot be ordered and possess no numerical qualities.

Instructions:

Identify the measurement(s)from the listaboveon marathonsthat place individuals in nonnumerical categories.

Step 2:Identify ordinal measurements.

Ordinal measurements represent a higher level than nominal measurements. Data is this category can be ordered, butmathematicaldifferences between data values do not make sense.

Example:

Considering the study of company employees, another variable in the study may be position in the management hierarchy, such asLevel 0 (hourly workers),Level 1 (low-level management), Level 2 (general management), and Level 3 (executives).This variable is ordinal because it allows employees to be ordered by rank, but mathematical differences between data valueshave no significant meaning. An executive is two levels above a low-level manager, and a general manager is two levels above an hourly worker, but these differences do not provide any meaningful information.

Instructions:

Identify the measurement(s)from the liston marathonswith data that canbe ordered but that have differences that cannot be determined or do not have anysignificantmeaning.

Step 3:Identify interval measurements.

Interval measurements represent a level of measurement higher than both nominal and ordinal measurements. Data is this category can be ordered and mathematical difference between data values have meaning.

Example:

If the year in which an employee joined the company is included in the study, this variable is an example of an interval measurement. Years can be ordered and differences in years make sense. It is meaningful to identify that one employee has worked at the company for 10 years longer than another, for example.

Instructions:

Identify the measurement(s) from the liston marathonswith data that can be ordered and differences in data values that make sense.

Step 4:Identify ratio measurements.

Ratio measurements represent the highest level of measurement. Data in this category can be ordered, and both differences in data values and ratios of data values can be computed and have meaning.

Example:

If the study of employees includes gathering data on the salaries of employees, this variable is an example of a ratio measurement. Salaries can be ordered and compared by differences and ratios. It makes sense to state that one employee makes a specific amount more or less than another employee. It also makes sense to state that one employee makes twice as much as another employee (a ratio of salaries).

Instructions:

Identify the measurement(s) from the liston marathonswith data that can be ordered and compared with differences and ratios.

Exercise 1:A national survey asked 5000 U.S. employed adults how far, in miles, they commute to work.

(a) Identify the variable.

(b) Is the variable quantitative or qualitative?

(c) What is the implied population?

Step 1:Identify the variable.

When designing a study, some of the first decisions we need to make are what to measure and who to include. A variable is the measured characteristic or feature of the included individuals.

Example:

If a study is being conducted on professional cyclists, variables might be age, weight, muscle mass, height,nationality, gender,and so on.

Instructions:

State the variableinthecommutingstudyabove.

Step 2:Determine if the variable is quantitative or qualitative.

A variable can be quantitative, meaning numerical, or qualitative, meaning categorical. Identifying if a variable is quantitative or qualitative is important for knowing which statistical methods can be used to analyze the data.

Example:

Variables like nationality and gender are qualitative. These variables do not have numerical attributes and simply place individuals in one of several categories or groups. Variables like age, height, and weight are quantitative. These variables are measured numerically.

Instructions:

Identify whether the variable of thecommutingstudy is quantitative or qualitative.

Step 3:Identify the implied population.

Collecting data from every individual of interest is often unrealistic, so samples are used. Statistics gathered from the study of a sample of individuals may be useful to describe the entire population (all of the individuals of interest).Understanding the difference between the population and the sample is crucial to properly interpret statistical results.

Example:

In a study of professional cyclists, perhaps data is collected from only 100 cyclists that are representative of all professional cyclists. In this case the population, or all individuals of interest, is the collection of all professional cyclists. The sample is the group of 100 cyclists that are included in the study.

Instructions:

Based on the description of thecommutingstudy, determine the population, or all the individuals of interest.

Exercise 2:Categorize these measurements associated with marathon running according to level: nominal, ordinal, interval, or ratio.

(a) ageof participant

(b)state or country of residency

(c)finishing time

(d)finishing position (place)

(e) year of first marathon

Step 1:Identify nominal measurements.

In addition to categorizing data or variables as quantitative or qualitative, we can categorize based on the level of measurement. This type of categorization helps us know which type of arithmetic is appropriate for the data.Nominal measurementsare categorical and are not able to be ordered.

Example:

A study is being conducted on the employees of a company.Onevariable of the study is the college or university from which the employee graduated. This variable is nominal because the colleges and universities cannot be ordered and possess no numerical qualities.

Instructions:

Identify the measurement(s)from the listaboveon marathonsthat place individuals in nonnumerical categories.

Step 2:Identify ordinal measurements.

Ordinal measurements represent a higher level than nominal measurements. Data is this category can be ordered, butmathematicaldifferences between data values do not make sense.

Example:

Considering the study of company employees, another variable in the study may be position in the management hierarchy, such asLevel 0 (hourly workers),Level 1 (low-level management), Level 2 (general management), and Level 3 (executives).This variable is ordinal because it allows employees to be ordered by rank, but mathematical differences between data valueshave no significant meaning. An executive is two levels above a low-level manager, and a general manager is two levels above an hourly worker, but these differences do not provide any meaningful information.

Instructions:

Identify the measurement(s)from the liston marathonswith data that canbe ordered but that have differences that cannot be determined or do not have anysignificantmeaning.

Step 3:Identify interval measurements.

Interval measurements represent a level of measurement higher than both nominal and ordinal measurements. Data is this category can be ordered and mathematical difference between data values have meaning.

Example:

If the year in which an employee joined the company is included in the study, this variable is an example of an interval measurement. Years can be ordered and differences in years make sense. It is meaningful to identify that one employee has worked at the company for 10 years longer than another, for example.

Instructions:

Identify the measurement(s) from the liston marathonswith data that can be ordered and differences in data values that make sense.

Step 4:Identify ratio measurements.

Ratio measurements represent the highest level of measurement. Data in this category can be ordered, and both differences in data values and ratios of data values can be computed and have meaning.

Example:

If the study of employees includes gathering data on the salaries of employees, this variable is an example of a ratio measurement. Salaries can be ordered and compared by differences and ratios. It makes sense to state that one employee makes a specific amount more or less than another employee. It also makes sense to state that one employee makes twice as much as another employee (a ratio of salaries).

Instructions:

Identify the measurement(s) from the liston marathonswith data that can be ordered and compared with differences and ratios.