Chapter 1, Problem 26CAP

To determine

Fill in the given table to identify the characteristics of each variable.

Answer to Problem 26CAP

The table for the characteristics of each variable is,

Variable	Qualitative vs Quantitative	Continuous vs Discrete	Scale of Measurement
Sex	Qualitative	Discrete	Nominal
Seasons	Qualitative	Discrete	Nominal
Time of day	Quantitative	Continuous	Ratio
Rating scale score	Quantitative	Discrete	Interval
Movie ratings (1 to 4 stars)	Quantitative	Discrete	Ordinal
Number of students in your class	Quantitative	Discrete	Ratio
Temperature (degrees Fahrenheit)	Quantitative	Continuous	Interval
Time (in minutes) to prepare dinner	Quantitative	Continuous	Ratio
Position standing in line	Quantitative	Discrete	Ordinal

Explanation of Solution

Quantitative variable:

The variable which is measured numerically and it is collected by counting or measuring is termed as quantitative variable. Also, the quantitative variable varies by amount.

Qualitative variable:

The variable which is represented as a label and describes the nonnumeric aspects of phenomena is termed as qualitative variable. Also, the qualitative variable varies by class.

Discrete variable:

If the variable measures whole units or categories that are not distributed along a continuum then it is termed as discrete variable.

Continuous variable:

If the variable measures a long a continuum, that is, it measures at any place beyond the decimal point then it is termed as continuous variable.

Nominal scale:

If measurements in which the numbers are assign to represent something or someone is termed as nominal scale.

Ordinal scale:

The measurements which convey the order or rank alone is said to be ordinal scale.

Interval scale:

The measurements which are distributed in equal units and have no true zero is said to be interval scale. In other words, the interval scale is equidistant but do not have true zero.

Ratio scale:

The measurements which are distributed in equal units and have a true zero is said to be ratio scale. In other words, the interval scale is equidistant and has a true zero. Also, the ratio scale is the most informative scale of measurement.

True zero:

The true zero is nothing on a scale of measurement when the value 0.

For sex:

The variable sex can be represented as labels and it describes nonnumeric aspects of phenomena. Therefore, the variable “sex” is qualitative.

The variable sex (male or female) is finite and it is collected by counting or measuring. Also, it is observed that sex is not a continuous series.

Therefore, the variable “sex” is discrete.

Here, it is observed that the nominal scale converts the sex into number. Therefore, the sex is measured by nominal scale.

For seasons:

The variable seasons (spring, summer, rainy, autumn, fall winter and winter) can be represented as labels and it describes nonnumeric aspects of phenomena. Therefore, the variable “seasons” is qualitative.

The variable ‘seasons’ is finite and it is collected by counting or measuring. Also, it is observed that seasons is not a continuous series.

Therefore, the variable “seasons” is discrete.

Here, it is observed that the nominal scale converts the seasons into number. Therefore, the season is measured by nominal scale.

For time of day:

The variable ‘time of day’ represents the numbers and that can be counted or measured. Thus, the variable time of day is quantitative.

The variable ‘time of day’ would be infinite or it is continuous series because it takes infinitely many values between any two times. Therefore, the variable ‘time of day’ is continuous variable.

Here, it is observed that the time of day is recorded. The time of day distributed in equal parts and it contains a value 0. Therefore, the variable ‘time of day’ is measured by ratio scale.

For rating scale score:

The variable ‘rating scale score’ represents the numbers and that can be counted or measured. Thus, the variable rating scale score is quantitative.

The variable ‘rating scale score’ is finite and it is collected by counting or measuring. Also, it is observed that rating scale score is not a continuous series.

Therefore, the variable “rating scale score” is discrete.

The rating scale score distributed in equal units and it does not true zero. Therefore, the variable rating scale score is measured by interval scale.

For movie rating (one to four stars):

The variable ‘movie rating (one to four stars)’ represents the numbers and that can be counted or measured. Thus, the variable movie rating (one to four stars) is quantitative.

The variable ‘movie rating (one to four stars)’ is finite and it is collected by counting or measuring. Also, it is observed that movie rating (one to four stars) is not a continuous series.

Therefore, the variable “movie rating (one to four stars)” is discrete.

The rating of the movie has a specific order that is based on a 4 star scale. The number 1 may represent ‘not good’, 2 may represent ‘average’, 3 may represent ‘good’ and 4 may represent ‘excellent’. It is clear that the values are arranged with the natural ordering.

Therefore, the variable movie rating (one to four stars) is measured by ordinal scale.

For number of students in a class:

The variable ‘number of students in a class’ represents the numbers and that can be counted or measured. Thus, the variable number of students in a class is quantitative.

The variable ‘number of students in a class’ is finite and it is collected by counting or measuring. Also, it is observed that ‘number of students in a class’ is not a continuous series.

Therefore, the variable ‘number of students in a class’ is discrete.

Here, it is observed that the ‘number of students in a class’ is recorded. The ‘number of students in a class’ distributed in equal parts and it contains a value 0. Therefore, the variable ‘number of students in a class’ is measured by ratio scale.

For temperature (degrees Fahrenheit):

The variable ‘temperature (degrees Fahrenheit)’ represents the numbers and that can be counted or measured. Thus, the variable temperature (degrees Fahrenheit) is quantitative.

The variable ‘temperature (degrees Fahrenheit)’ would be infinite or it is continuous series because it takes infinitely many values between any two degrees Fahrenheit. Therefore, the variable ‘temperature (degrees Fahrenheit)’ is continuous variable.

The temperature (degrees Fahrenheit) distributed in equal units and it does not have true zero. Therefore, the variable temperature (degrees Fahrenheit) is measured by interval scale.

For time (in minutes) to prepare dinner:

The variable ‘time (in minutes) to prepare dinner’ represents the numbers and that can be counted or measured. Thus, the variable time (in minutes) to prepare dinner is quantitative.

The variable ‘time (in minutes) to prepare dinner’ would be infinite or it is continuous series because it takes infinitely many values between any two minutes. Therefore, the variable ‘time (in minutes) to prepare dinner’ is continuous variable.

Here, it is observed that the time (in minutes) to prepare dinner is recorded. The time (in minutes) to prepare dinner distributed in equal parts and it contains a value 0. Therefore, the variable ‘time (in minutes) to prepare dinner’ is measured by ratio scale.

For position standing in line:

The variable ‘position standing in line’ represents the numbers and that can be counted or measured. Thus, the position standing in line is quantitative.

The variable ‘position standing in line’ is finite and it is collected by counting or measuring. Also, it is observed that ‘position standing in line’ is not a continuous series.

Therefore, the variable ‘position standing in line’ is discrete.

The position standing in line has a specific order. That is, the values are arranged with the natural ordering.

Therefore, the position standing in line is measured by ordinal scale.

Hence, the table for the characteristics of each variable is,

Variable	Qualitative vs. Quantitative	Continuous vs. Discrete	Scale of Measurement
Sex	Qualitative	Discrete	Nominal
Seasons	Qualitative	Discrete	Nominal
Time of day	Quantitative	Continuous	Ratio
Rating scale score	Quantitative	Discrete	Interval
Movie ratings (1 to 4 stars)	Quantitative	Discrete	Ordinal
Number of students in your class	Quantitative	Discrete	Ratio
Temperature (degrees Fahrenheit)	Quantitative	Continuous	Interval
Time (in minutes) to prepare dinner	Quantitative	Continuous	Ratio
Position standing in line	Quantitative	Discrete	Ordinal