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Chapter 1: Problem 27

Determine whether the quantitative variable is discrete or continuous. High temperature on a randomly selected day in Memphis, Tennessee

Short Answer

Expert verified
The high temperature on a randomly selected day in Memphis, Tennessee is a continuous variable.

Step by step solution

01

Understanding Discrete Variables

A discrete variable is one that can take on a finite or countably infinite number of values. These values are distinct and separate; there is no in-between value. Examples include the number of students in a classroom, the number of cars in a parking lot, or the number of pages in a book.
02

Understanding Continuous Variables

A continuous variable, on the other hand, can take on an infinite number of values within a given range. These values are not restricted to separate values and can include any fraction or decimal. Examples include a person's height, the amount of milk in a jug, or the time it takes to run a race.
03

Analyzing the Given Variable

Consider the high temperature on a randomly selected day in Memphis, Tennessee. This variable can be any value within a range and can include decimals or fractions (e.g., 75.3掳F, 80.5掳F). This implies that the temperature is not limited to distinct, separate values but can take on any value within a range.
04

Conclusion

Since the high temperature can take on any value within a given range and is not restricted to distinct, separate values, it is a continuous variable.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quantitative Variables
Quantitative variables are those that can be measured and expressed numerically. They are used to quantify characteristics, attributes, or properties. For instance, variables like height, weight, and temperature can be measured and given a numerical value. Quantitative variables provide valuable information because they allow for calculations and statistical analysis. These variables fall into two categories: discrete and continuous. Understanding the differences between these types is crucial for accurate data analysis and application.
Discrete Variables
Discrete variables are countable in a finite or countably infinite set of values. This means you can't have a value between two distinct points. For example, if you're counting the number of students in a classroom, you can't have 25.5 students - it's either 25 or 26. Discrete variables work well for items that can only be whole numbers or distinct categories, such as:
  • The number of cars in a parking lot.
  • The number of chapters in a book.
  • The count of apples in a basket.
These numbers are definite and non-divisible.
Continuous Variables
Continuous variables, in contrast, can take any value within a given range. That means the values can be fractional and have infinite possibilities within the interval. For example, consider measuring the high temperature of a randomly selected day in Memphis, Tennessee. The temperature can be 75.3掳F, 80.5掳F, or any value in between. Continuous variables are used to represent measurements that can have more precision and detail, such as:
  • The height of a person (e.g., 5.9 feet).
  • The amount of time to complete a task (e.g., 23.75 seconds).
  • The weight of a bag of flour (e.g., 2.5 kg).
This allows for more nuanced data analysis and representation.
Temperature Measurement
Temperature measurement is a classic example of a continuous variable. When you measure temperature, the readings can be any value within a possible range, allowing for very precise measurements. For instance, on a randomly selected day in Memphis, Tennessee, the high temperature might be a decimal value like 78.6掳F. Because temperature can vary smoothly and doesn't jump between values without covering the intermediate ones, it is classified as a continuous variable. Accurate temperature measurement is essential in fields like meteorology, science, and engineering. These precise readings help in understanding patterns, making predictions, and conducting experiments.

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Most popular questions from this chapter

A research objective is presented. For each, identify the population and sample in the study. A community college notices that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks how many hours per week each works.

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