Question

Quantitative or Qualitative? Identify each variable as quantitative or qualitative: a. Ethnic origin of a candidate for public office b. Score \((0-100)\) on a placement examination c. Fast-food establishment preferred by a student (McDonald's, Burger King, or Carl's Jr.) d. Mercury concentration in a sample of tuna

Short answer

Question: Classify each of the following variables as either quantitative or qualitative: a. Ethnic origin b. Score on a placement examination c. The fast-food establishment preferred by a student d. Mercury concentration in a sample of tuna Answer: a. Ethnic origin: Qualitative b. Score on a placement examination: Quantitative c. Fast-food establishment preference: Qualitative d. Mercury concentration in tuna: Quantitative

Step-by-step solution

Identifying Variable Types #

First, let's identify each variable as either quantitative or qualitative based on the definitions provided above: a. Ethnic origin represents categorical data, as it belongs to different categories of ethnic roots. So, it is a qualitative variable. b. Score on a placement examination represents numerical data, since the scores can be compared using arithmetic operations. It is therefore a quantitative variable. c. The fast-food establishment preferred by a student represents categorical data, as it belongs to different categories of fast-food restaurants. So, it is a qualitative variable. d. Mercury concentration in a sample of tuna represents numerical data, as it can be compared using arithmetic operations. It is therefore a quantitative variable.

Final Classification #

To summarize the classification of variables: a. Ethnic origin: Qualitative b. Score on a placement examination: Quantitative c. Fast-food establishment preference: Qualitative d. Mercury concentration in tuna: Quantitative

Key concepts

Quantitative Variables

Quantitative variables are all about numbers! They are used when collecting data in the form of actual numbers that can be measured and counted. This type of data is very useful because you can do arithmetic operations on them, like addition, subtraction, multiplication, and division. Some common examples are height, weight, age, and test scores. For instance, when we look at the score (from 0 to 100) on a placement exam, it fits perfectly as a quantitative variable because it is a numerical measurement. Additionally, it can be compared and analyzed using various statistical techniques. Quantitative data provides precise measurements, which makes it invaluable in scientific research and everyday decision-making.

Qualitative Variables

Qualitative variables, unlike quantitative variables, do not deal with numbers. Instead, they focus on characteristics or qualities that can't generally be measured or compared in terms of size or amount. These are all about categories or descriptions rather than precise figures. For example, when we think about ethnic origin or a student's preference for a certain fast-food restaurant, we're dealing with qualitative variables. These help us understand the distinct categories that entities or individuals fall into, like selecting between McDonald's, Burger King, or Carl's Jr. in our exercise. Consider them as data points that can tell us about traits like color, shape, or type, which help to classify different types within a group.

Categorical Data

Categorical data is a type of qualitative data and it's centered around concepts and ideas that fit into different categories. This data divides things into labeled groups or classes without involving numbers. It's like sorting beans into different jars based on color. In the exercise, the ethnic origin of candidates and the preference for a fast-food establishment are great examples of categorical data. Such data is crucial in studies and surveys when understanding distinctions or preferences among people or objects is the goal. Categorical data can be divided into two main types: nominal and ordinal.

• Nominal data represents categories that do not have an inherent order. For instance, ethnic origin or the type of fast-food chain belongs to this type.
• Ordinal data arrange categories in a specific order, such as a rating scale (good, better, best).

Numerical Data

Numerical data is the backbone of quantitative research, focusing on numbers that you can play with mathematically. This data is all about numbers you can count or measure, and it gives us the ability to perform calculations and statistical analysis. The mercury concentration in a tuna sample from our example is numerical data, as it offers a precise measurement that can be expressed in numbers. Numerical data is often split into two categories: discrete and continuous.

• Discrete data counts numbers in whole figures. Examples include the number of people in a room or test scores.
• Continuous data can be measured on a finer scale, like temperature or the mercury concentration in tuna.

This type of data is powerful because it takes advantage of mathematical tools to perform analyses, helping us discover patterns, trends, or relationships within the information.