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Chapter 1: Problem 14

Using data from such publications as the Statistical Abstract of the United States, Forbes, or any news source, give examples of variables measured with nominal, ordinal, interval, and ratio scales.

Short Answer

Expert verified
Nominal: Industry type; Ordinal: Customer satisfaction ratings; Interval: Temperature; Ratio: Income.

Step by step solution

01

Understanding Scale Types

Before we find examples, let's identify what each measurement scale means. Nominal scale is used for labeling variables without any quantitative value. Ordinal scale has ordered categories, but the intervals between them are not guaranteed to be equal. Interval scale has ordered categories with equal intervals, but no true zero point. Lastly, ratio scale has all the properties of an interval scale with a meaningful zero point.
02

Finding Nominal Scale Examples

Data categorized based on names or labels are measured on a nominal scale. Examples could be the different types of industries (like Healthcare, Technology, Manufacturing) or categories of political parties.
03

Finding Ordinal Scale Examples

Data categorized based on a meaningful order. For example, customer satisfaction ratings (Poor, Fair, Good, Excellent) or class rankings (Freshman, Sophomore, Junior, Senior).
04

Finding Interval Scale Examples

Data with a meaningful order and equal intervals but no true zero point. For example, temperature measured in Celsius or Fahrenheit, where zero does not indicate absence of temperature.
05

Finding Ratio Scale Examples

Data that represent quantities and have a true zero point. Examples include height, weight, or income where zero indicates no height, weight, or income.

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Key Concepts

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

Nominal Scale
The nominal scale is the most basic measurement scale, often used for classification and labeling purposes. It helps to identify or categorize data but does not offer any quantitative value or meaningful order. Think of it as the labels on a selection of colorful boxes鈥攊t's about distinguishing one item from another without implying any sort of preference or ranking.

Nominal data can include:
  • Types of Fruits: Apples, oranges, bananas.
  • Political Affiliation: Democrat, Republican, Independent.
  • Departments in a Store: Toys, Electronics, Clothing.
Using nominal measurements allows for effective grouping and sorting, making it easier to handle and reference different kinds of data.
Ordinal Scale
With the ordinal scale, data is categorized in a particular order but without knowing the magnitude of difference between each category. This scale ranks data, placing items in a specific sequence, but doesn't specify how much better or worse one item is than another.

Examples of ordinal scale data include:
  • Customer Satisfaction: Very Dissatisfied, Dissatisfied, Neutral, Satisfied, Very Satisfied.
  • Education Levels: High School, Bachelor's Degree, Master's Degree, Doctorate.
  • Movie Ratings: 1 Star, 2 Stars, 3 Stars, 4 Stars, 5 Stars.
This type of data is particularly useful for surveys and questionnaires, where responses are ranked but the intervals between responses are unknown.
Interval Scale
The interval scale is an extension of the ordinal scale, featuring equally spaced intervals between values. This allows for not only ranking the data but also understanding the difference between entries.

However, it lacks a true zero point, which means the absence of the characteristic is not indicated by a zero value. Some common examples include:
  • Temperature: Measured in Celsius or Fahrenheit, where zero does not signify 'no temperature'.
  • Calendar Years: The difference between 2000 and 2020 is the same as between 1990 and 2010, but there is no "year zero" indicating a total absence of time.
Interval scales are useful in scenarios where operations of addition and subtraction are relevant, making them great for statistical analysis and the calculation of meaningful averages.
Ratio Scale
The ratio scale has all the characteristics of the interval scale, but with the added feature of a true zero point. This true zero allows for a statement of 'none' or 'absence' of a property. The zero value is crucial as it indicates a total lack of the measured characteristic, enabling a full range of mathematical operations

Examples include:
  • Weight: A weight of zero means no weight at all.
  • Height: A height of zero implies no height.
  • Income: An income of zero suggests no income earned.
Ratio scale is the most informative mathematical scale as it allows comparisons of both differences and proportions, which means you can say how many times one value is greater than another. This scale is widely used in most scientific and engineering disciplines for precise measurements.

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Most popular questions from this chapter

Place these variables in the following classification tables. For each table, summarize your observations and evaluate if the results are generally true. For example, salary is reported as a continuous quantitative variable. It is also a continuous ratio-scaled variable. a. Salary b. Gender c. Sales volume of MP3 players d. Soft drink preference e. Temperature f. SAT scores g. Student rank in class h. Rating of a finance professor i. Number of home video screens

For the following situations, would you collect information using a sample or a population? Why? a. Statistics 201 is a course taught at a university. Professor Rauch has taught nearly 1,500 students in the course over the past 5 years. You would like to know the average grade for the course. b. As part of a research project, you need to report the average profit as a percentage of revenue for the #1-ranked corporation in the Fortune 500 for each of the last 10 years. c. You are looking forward to graduation and your first job as a salesperson for one of five large pharmaceutical corporations. Planning for your interviews, you will need to know about each company's mission, profitability, products, and markets. d. You are shopping for a new MP3 music player such as the Apple iPod. The manufacturers advertise the number of music tracks that can be stored in the memory. Usually, the advertisers assume relatively short, popular songs to estimate the number of tracks that can be stored. You, however, like Broadway musical tunes and they are much longer. You would like to estimate how many Broadway tunes will fit on your MP3 player.

Refer to the North Valley Real Estate data, which report information on homes sold in the area last year. Consider the following variables: selling price, number of bedrooms, township, and mortgage type. a. Which of the variables are qualitative and which are quantitative? b. How is each variable measured? Determine the level of measurement for each of the variables.

Explain the difference between qualitative and quantitative variables. Give an example of qualitative and quantitative variables.

Explain the difference between a sample and a population.
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