Chapter 2, Problem 35CE

Below are five questions from a survey of MBA students Answers were written in the blank at the left of each question. For each question, state the data type (categorical, discrete numerical, or continuous numerical) and measurement level (nominal, ordinal, interval, ratio). Explain your reasoning. If there is doubt discuss the alternatives.

To determine

Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.

Answer to Problem 35CE

The data type of the question “What is the age of the car you usually drive?” is continuous numerical.

The question has ratio measurement level.

Explanation of Solution

A survey is conducted on MBA students. The given question is, “What is the age of the car you usually drive? (years)”.

Categorical data:

The type of data that naturally take non-numerical values, such as words that can classify or name the data points based on their quality, are called qualitative or categorical data. In order to facilitate the use of statistical methods on categorical data, a commonly used process used is coding, where each value of the categorical variable is coded or represented using a unique number.

Discrete numerical data:

The type of data that can take a countable number of distinct numerical or quantitative values is called a discrete numerical data.

Continuous numerical data:

The type of data that can take an uncountable or infinite number of numerical or quantitative values within any given interval is called a continuous numerical data.

The age of a student’s car can take infinite values within a given interval.

Hence, the data type of the question “What is the age of the car you usually drive?” is continuous numerical.

Nominal measurement:

Nominal measurement is the most basic form of measurement that names or categorizes or classifies data. It is the weakest and easiest form of measurement.

Ordinal measurement:

Ordinal measurement is the measurement that ranks the data in a logical manner. It can be used when a natural ordering is present in the data to give the relative position of one object with respect to another. Numerical values can be assigned to the orders of the data, even when the data values are not naturally numerical. The properties of nominal measurement are applicable for ordinal measurement.

Interval measurement:

Interval measurement is the measurement that can be applied to data that naturally occur in the numerical form and counting of these values is logical. This scale of measurement does not have a meaningful “zero” value. However, the difference between any two points on the scale is meaningful. The operations of addition and subtraction on this scale are meaningful. The properties of nominal and ordinal measurements are applicable for interval measurement.

Ratio measurement:

Ratio measurement is the strongest form of measurement that can be applied to data that naturally occur in the numerical form and counting of these values is logical. This scale of measurement has a meaningful “zero” value. The operations of addition, subtraction, multiplication and division on this scale are meaningful. The properties of nominal, ordinal and interval measurements are applicable for ratio measurement.

The age of a car can be measured. Moreover, the value zero is also logical as the age. The operations of addition, subtraction, multiplication and division can be logically performed on this variable.

Hence, the question “What is the age of the car you usually drive?” has ratio measurement level.

To determine

Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.

Answer to Problem 35CE

The data type of the question “About how many times in the past year did you attend formal religious services?” is discrete numerical.

The question has ratio measurement level.

Explanation of Solution

The given variable is, “About how many times in the past year did you attend formal religious services?”

The number of times a student attended a formal religious service in any given year takes distinct numerical values, which are countable in nature. This number cannot take a fractional value.

Hence, the data type of the question “About how many times in the past year did you attend formal religious services?” is discrete numerical.

The number of times a student attended a formal religious service in any given year can be counted. Moreover, the value zero is also logical as the number of services attended by a student. The operations of addition, subtraction, multiplication and division can be logically performed on this variable.

Hence, the question “About how many times in the past year did you attend formal religious services?” has ratio measurement level.

To determine

Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.

Answer to Problem 35CE

The data type of the question “How often do you read a daily newspaper?”  is categorical.

The question has either ordinal or interval measurement level..

Explanation of Solution

The given variable is, “How often do you read a daily newspaper? (0 = Never, 1 = Occasionally, 2 = Regularly)”

The frequency with which a student reads newspaper is ordered in three categories, which are assigned numerical values. It is not logical to apply mathematical operations to these values.

Hence, the data type of the question “How often do you read a daily newspaper?” is categorical.

The frequency of reading newspaper for a student can be ordered from high to low or from low to high. It can be ranked and assigned numerical values. However, application of mathematical operations is not logical on these values. In this sense, the question “How often do you read a daily newspaper?” has ordinal measurement level.

Likert scale:

The Likert scale is a scale that assigns or codes equidistant values to the ordered categories of a data set. If it is logical to assign such equidistant values to the ordered categories, then an ordinal scale data can be expressed as an interval scale data.

Now, the ordered frequency of reading newspaper for a student can be expressed logically as equidistant values, as on a Likert scale. The operations of addition and subtraction can be logically performed on such variable. However, there is no absolute zero value of these frequencies. One may or may not choose a zero value at their discretion, without any hard-and-fast rule. In this sense, the question “How often do you read a daily newspaper?” has interval measurement level.

To determine

Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.

Answer to Problem 35CE

The data type of the question “Can you conduct simple transactions in a language other than English?”  is categorical.

The question has nominal measurement level.

Explanation of Solution

The given variable is, “Can you conduct simple transactions in a language other than English? (0 = No, 1 = Yes)”

The ability of a student to conduct simple transactions in a language other than English simply classifies or categorizes the student. It does not take any numerical values naturally.

Hence, the data type of the question “Can you conduct simple transactions in a language other than English?” is categorical.

The ability of a student to conduct simple transactions in a language other than English classifies or categorizes the student. Even when numbers are assigned to such an ability, these cannot be ranked in a logical order. Moreover, it is not logical to perform mathematical operations on such numbers.

Hence, the question “Can you conduct simple transactions in a language other than English?” has nominal measurement level.

To determine

Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.

Answer to Problem 35CE

The data type of the question “How often do you exercise (aerobics, running, etc.)?” is categorical.

The question has ordinal measurement level.

Explanation of Solution

The given variable is, “How often do you exercise (aerobics, running, etc.)? (0 = Not at All, 1 = Sometimes, 2 = Regularly)”.

The frequency with which a student exercises is ordered in three categories, which are assigned numerical values. It is not logical to apply mathematical operations to these values.

Hence, the data type of the question “How often do you exercise (aerobics, running, etc.)?” is categorical.

The frequency of exercising of a student can be ordered from high to low or from low to high. It can be ranked and assigned numerical values. However, application of mathematical operations is not logical on these values. In this sense, the question “How often do you exercise (aerobics, running, etc.)?” has ordinal measurement level.

Now, the ordered frequency of exercising of a student can be expressed logically as equidistant values, as on a Likert scale. The operations of addition and subtraction can be logically performed on such variable. However, there is no absolute zero value of these frequencies. One may or may not choose a zero value at their discretion, without any hard-and-fast rule. In this sense, the question “How often do you exercise (aerobics, running, etc.)?” has interval measurement level.