Question

Discrete or Continuous? Identify the following quantitative variables as discrete or continuous: a. Population in a particular area of the United States b. Weight of newspapers recovered for recycling on a single day c. Time to complete a sociology exam d. Number of consumers in a poll of 1000 who consider nutritional labeling on food products to be important

Short answer

Question: Identify whether the following quantitative variables are discrete or continuous: a. Population in a particular area of the United States b. Weight of newspapers recovered for recycling on a single day c. Time to complete a sociology exam d. Number of consumers in a poll of 1000 who consider nutritional labeling on food products to be important Answer: a. Discrete b. Continuous c. Continuous d. Discrete

Step-by-step solution

a. Population in a particular area of the United States

As the population consists of a whole number of people without fractional parts, it is a discrete variable.

b. Weight of newspapers recovered for recycling on a single day

The weight of newspapers can be expressed in decimals and fractions (any value within a given range) and isn't restricted to whole numbers, as a result, it is a continuous variable.

c. Time to complete a sociology exam

The time taken can be expressed in decimals and fractions (e.g., 1.5 hours, 15.7 minutes) and is not limited to whole numbers. Thus, it is a continuous variable.

d. Number of consumers in a poll of 1000 who consider nutritional labeling on food products to be important

The number of consumers must be a whole number without any fractional parts (you can't have a "fraction" of a person). Therefore, it is a discrete variable.

Key concepts

Discrete Variables

Discrete variables are a type of quantitative variable that take on specific, distinct values. These values are separate and can be counted or enumerated. Discrete variables are characterized by a lack of fractional parts, meaning they only include whole numbers. For example, when counting people or objects, we usually deal with discrete variables.

Some key features of discrete variables:

• Values are distinct and separate from each other.
• There are no "in-between" values. You cannot have a fractional value in a discrete set.
• Typically, they answer the question of 'how many'.

In the context of the original exercise, both the "population in a particular area" and the "number of consumers in a poll" represent discrete variables. This is because these scenarios involve counting individuals, which results in whole numbers only.

Continuous Variables

Continuously variable data do not have specific, separate values and can, theoretically, take on an infinite number of values within a given range. This is because continuous variables are capable of fractional values. As a result, when measuring continuous variables, you often deal with precise or approximate numbers, rather than whole counts.

Some characteristics of continuous variables include:

• They can take any value within a certain range (including fractional values).
• Useful for measurements such as time, weight, height, and distance.
• They help answer questions related to 'how much' or 'how long'.

In the original exercise, both "the weight of newspapers recovered for recycling" and "time to complete a sociology exam" are examples of continuous variables. This is because these scenarios allow for decimals and fractional values, such as weighing a newspaper to 0.5 pounds or timing an exam to 15.7 minutes.

Data Classification

Data classification is essential in statistical analysis because it enables researchers to organize data into meaningful categories. This organization helps in selecting proper analytical methods, leading to accurate insights and conclusions.

• Quantitative Data: This type includes numbers and can be further split into discrete and continuous variables.
• Qualitative Data: This type consists of non-numerical values and represents categories or labels, such as names or types.

Quantitative data classification divides data into discrete or continuous variables, depending on if the values can or cannot take fractional numbers. The ability to distinguish between these types helps in choosing statistical procedures, such as the calculations of mean, median, or mode, specific to the data type. Understanding data classification ensures correct interpretation and improves the reliability of any conclusions. In practical terms, correctly classifying whether a piece of information is a discrete or continuous variable allows us to use the right tools for analysis, enhancing the quality of research outcomes.