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Chapter 1: Problem 28

Determine whether the quantitative variable is discrete or continuous. Volume of water lost each day through a leaky faucet

Short Answer

Expert verified
The volume of water lost each day through a leaky faucet is a continuous variable.

Step by step solution

01

Understand the Variables

Consider what a quantitative variable is. A quantitative variable represents amounts or quantities and can be measured or counted.
02

Define Discrete Variables

Discrete variables are those that can only take specific values, such as whole numbers. They are countable, like the number of students in a classroom.
03

Define Continuous Variables

Continuous variables can take any value within a range and can be measured to any desired level of precision, such as temperature or height.
04

Identify Type of Measurement

Consider how the volume of water lost each day is measured. It can be any value within a range and can be measured very precisely using units like liters or milliliters.
05

Determine the Variable Type

Since the volume of water lost each day can take any value within a range and is measurable to a precise level, 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.

Discrete Variables
Discrete variables are types of quantitative variables that represent countable quantities. They can only take specific, separate values. For instance, the number of students in a classroom or the number of cars passing through a toll booth each hour are discrete variables.

Key characteristics of discrete variables include:

  • They are countable.
  • They typically involve whole numbers.
  • They cannot take on fractional or decimal values.
Discrete variables often answer the question 'How many?' and are especially useful in scenarios where precise, whole number counts are necessary.
Continuous Variables
Continuous variables are quantitative variables that can take any value within a range. They are measurable and can be infinitely divided into finer and finer increments. Examples of continuous variables include the height of a person, the amount of time needed to complete a task, and critical to our exercise, the volume of water lost through a leaky faucet.

Characteristics of continuous variables include:

  • They are measurable and can take any value within a given range.
  • They can include fractional and decimal values.
  • They can be infinitely divided, allowing precise measurement.
Think of continuous variables as answering the question 'How much?' and being particularly useful for measurements requiring detailed precision.
Measurement Precision
Measurement precision refers to the ability to obtain consistent and exact measurements. This concept is crucial when dealing with continuous variables because precision determines the smallest unit of measurement that we can reliably distinguish. The precision might be in liters, milliliters, or even smaller units.

Key aspects of measurement precision include:

  • The smallest unit of measurement you can reliably use.
  • The consistency and repeatability of a measurement.
  • How close the measured value is to the true value.
In the context of our exercise, the volume of water lost each day through a leaky faucet can require high precision, especially if the leak is minimal and needs to be measured in milliliters for accuracy.

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Most popular questions from this chapter

Researchers wish to know if there is a link between hypertension (high blood pressure) and consumption of salt. Past studies have indicated that the consumption of fruits and vegetables offsets the negative impact of salt consumption. It is also known that there is quite a bit of person-to-person variability as far as the ability of the body to process and eliminate salt. However, no method exists for identifying individuals who have a higher ability to process salt. The U.S. Department of Agriculture recommends that daily intake of salt should not exceed 2400 mg. The researchers want to keep the design simple, so they choose to conduct their study using a completely randomized design. (a) What is the response variable in the study? (b) Name three factors that have been identified. (c) For each factor identified, determine whether the variable can be controlled, cannot be controlled, or should be manipulated. If a factor cannot be controlled, what should be done to reduce variability in the response variable? (d) How many treatments would you recommend? Why?

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