Question

Continuous or Discrete, again Identify each variable as continuous or discrete: a. Weight of two dozen shrimp b. A person's body temperature c. Number of people waiting for treatment at a hospital emergency room d. Number of properties for sale by a real estate agency e. Number of claims received by an insurance company during one day

Short answer

Question: Determine if each given variable is continuous or discrete. a. Weight of two dozen shrimp b. A person's body temperature c. Number of people waiting for treatment at a hospital emergency room d. Number of properties for sale by a real estate agency e. Number of claims received by an insurance company during one day Answer: a. Continuous b. Continuous c. Discrete d. Discrete e. Discrete

Step-by-step solution

a. Weight of two dozen shrimp

The weight of two dozen shrimp can take any value within a range, depending on the size and weight of each individual shrimp. Weight is a continuous variable.

b. A person's body temperature

A person's body temperature can take any value within a given range and is not restricted to integer values. Therefore, body temperature is a continuous variable.

c. Number of people waiting for treatment at a hospital emergency room

The number of people waiting for treatment at a hospital emergency room can only take whole numbers - you can't have a fraction of a person waiting. Therefore, this variable is discrete.

d. Number of properties for sale by a real estate agency

An agency can have a whole number of properties for sale, but not a fraction of a property. The number of properties for sale is a discrete variable.

e. Number of claims received by an insurance company during one day

The number of claims received by an insurance company during one day can only be whole numbers, as each claim is an individual event. Thus, this variable is discrete.

Key concepts

Continuous Variables

Continuous variables are variables that can take on an infinite number of values within a specified range. These variables can include decimals and fractions, meaning there are no gaps or jumps between the possible values. For instance, measurements like weight, height, and temperature are typically continuous. When we refer to the weight of two dozen shrimp, the weight can vary continuously depending on factors like the size of each shrimp. There isn't a fixed interval or a limited set of possibilities; it can be, for example, 1.234 kilograms or 1.235 kilograms. Similarly, a person’s body temperature can also be considered a continuous variable because it can vary within a range and include fractions like 36.5°C or 37.2°C. Therefore, continuous variables are often measured rather than counted, providing a more nuanced data set.

Discrete Variables

Discrete variables differ from continuous variables in that they can only take on specific, separate values. This is often because these values need to fall within distinct categories or be counted as whole numbers. For example, the number of people waiting at a hospital emergency room is a discrete variable. You cannot have 3.5 people waiting; it must be a whole number—this makes it countable, which is a characteristic of discrete variables.

• Number of houses for sale by a real estate agency
• Number of insurance claims received during a day

Both are examples of discrete variables. They represent counts of items or events where intermediate values don't exist and where the data is naturally segregated into equal intervals. These variables give straightforward numerical data, making them easier to handle and often quicker to analyze.

Variable Identification

The process of variable identification involves recognizing the type of variable you are working with, as knowing whether a variable is continuous or discrete will help in selecting the appropriate statistical methods for analysis. It determines how the data should be collected, organized, and interpreted.

• Continuous variables are typically identified in situations where measurements are possible, like weight or temperature.
• Discrete variables are often found in situations where counting is necessary, such as the number of items sold or events happening.

Correctly identifying the type of variable can influence the choice of statistical measures, such as mean or median, and how the data is visualized, whether through histograms or bar charts. Understanding the nature of these variables is foundational in fields like data analysis, economics, and social sciences, as it guides the interpretation of the data and the insights that can be drawn from it.