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Chapter 5: Problem 15

State whether the variable is discrete or continuous. The temperature of the water in Lake Erie

Short Answer

Expert verified
The temperature of the water is a continuous variable.

Step by step solution

01

Identify the Nature of the Variable

A temperature measurement, like the temperature of the water in Lake Erie, results in a numerical value that can vary within a range. The key question is whether this range is countable or uncountable.
02

Determine Range Characteristics

Consider the possible values of the water temperature. Temperatures can vary continuously and are not restricted to a countable number of values. This means that between any two temperature measurements, there can be an infinite number of possible temperatures.
03

Classify the Variable

Since there is an infinite number of possible values within any interval of temperature measurements, and these values can be expressed with decimals, the variable is considered continuous.

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Key Concepts

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

Discrete Variables
To understand discrete variables, picture them as a set of separate or distinct values. These values are countable and often finite, like the number of students in a classroom or the number of books on a shelf. Unlike continuous variables, which can take on any value within a range, discrete variables jump from one value to the next without spanning a continuum. \[ n = 0, 1, 2, \dots \]Some key points about discrete variables include:
  • They are countable: You can list all possible values individually.
  • Each measurement is distinct, with no intermediate values possible within a given range.
  • Examples include things like the roll of a dice or number of cars passing through a tollbooth.
Recognizing whether a variable is discrete can help in deciding which statistical methods to use for analysis, as these will differ from those used with continuous data.
Temperature Measurement
When we talk about temperature measurement, we usually think of numerical values that describe how hot or cold something is. In the context of our exercise, we're considering the temperature of water in Lake Erie. Temperature measurements represent continuous data. Here鈥檚 why:
  • The readings can vary continuously within a defined range.
  • Temperatures are expressed as decimal numbers, allowing for an infinite number of possible values between any two measured temperatures.
  • For example, between 20掳C and 21掳C, temperatures like 20.5掳C or 20.25掳C are possible.
This ability to take on any value within a given range distinguishes continuous variables from discrete ones, making temperature measurement a prime example of the former.
Statistical Classification
Statistical classification involves grouping data into categories based on their characteristics. This process is crucial in accurately analyzing and interpreting data sets. In general, classification helps in:
  • Determining the type of analysis and statistical tests to employ.
  • Understanding the nature of the data: continuous, discrete, nominal, or ordinal.
  • Making predictions, identifying trends, and spotting outliers in data.
The classification between continuous and discrete data is a quintessential task in statistics. Continuous data, like temperature or height, can be any value within a range. Discrete data, on the other hand, consists of specific distinct values. By properly classifying data, statisticians can ensure accurate data interpretation and result communication, which is essential for scientific research and decision-making processes.

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Most popular questions from this chapter

A school newspaper staff is comprised of 5 seniors, 4 juniors, 5 sophomores, and 7 freshmen. If 4 staff members are chosen at random for a publicity photo, what is the probability that there will be 1 student from each class?

According to Mendel's theory, if tall and colorful plants are crossed with short and colorless plants, the corresponding probabilities are \(\frac{9}{16}, \frac{3}{16}, \frac{3}{16},\) and \(\frac{1}{16}\) for tall and colorful, tall and colorless, short and colorful, and short and colorless, respectively. If 8 plants are selected, find the probability that 1 will be tall and colorful, 3 will be tall and colorless, 3 will be short and colorful, and 1 will be short and colorless.

Assume all variables are binomial. (Note: If values are not found in Table B of Appendix \(A,\) use the binomial formula. Fiftythree percent of all persons in the U.S. population have at least some college education. Choose 10 persons at random. Find the probability that a. Exactly one-half have some college education b. At least 5 do not have any college education c. Fewer than 5 have some college education

Which of the following are binomial experiments or can be reduced to binomial experiments? a. Testing one brand of aspirin by using 10 people to determine whether it is effective b. Asking 100 people if they smoke c. Checking 1000 applicants to see whether they were admitted to White Oak College d. Surveying 300 prisoners to see how many different crimes they were convicted of e. Surveying 300 prisoners to see whether this is their first offense

A shipment of 24 computer keyboards is rejected if 4 are checked for defects and at least 1 is found to be defective. Find the probability that the shipment will be returned if there are actually 6 defective keyboards.
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