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Chapter 1: Problem 39

What type of measure scale is being used? Nominal, ordinal, interval or ratio. a. High school soccer players classified by their athletic ability: Superior, Average, Above average b. Baking temperatures for various main dishes: 350, 400, 325, 250, 300 c. The colors of crayons in a 24-crayon box d. Social security numbers e. Incomes measured in dollars f. A satisfaction survey of a social website by number: 1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied g. Political outlook: extreme left, left-of-center, right-of-center, extreme right h. Time of day on an analog watch i. The distance in miles to the closest grocery store j. The dates 1066, 1492, 1644, 1947, and 1944 k. The heights of 21鈥�65 year-old women l. Common letter grades: A, B, C, D, and F

Short Answer

Expert verified
a. Ordinal, b. Interval, c. Nominal, d. Nominal, e. Ratio, f. Ordinal, g. Ordinal, h. Interval, i. Ratio, j. Interval, k. Ratio, l. Ordinal.

Step by step solution

01

Understanding Scales of Measurement

There are four main scales of measurement: 1. Nominal: Categorizes data without a specific order. 2. Ordinal: Categorizes data with a specific order but no precise differences between ranks. 3. Interval: Ordered categories with meaningful differences, but no true zero. 4. Ratio: Ordered, meaningful differences between quantities, and a true zero exists.
02

Classifying Each Example

Let's classify each given example: a. High school soccer players by athletic ability (Superior, Average, Above average) - Ordinal scale since there is a meaningful order to the categories. b. Baking temperatures (350, 400, 325, 250, 300) - Interval scale since differences are meaningful but there is no true zero point. c. Colors of crayons - Nominal scale because they are categories without order. d. Social security numbers - Nominal scale as they are identifiers with no order. e. Incomes measured in dollars - Ratio scale as there is a true zero and meaningful comparisons. f. Satisfaction survey (1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied) - Ordinal scale due to the meaningful rank order. g. Political outlook (extreme left, left-of-center, right-of-center, extreme right) - Ordinal scale due to ordered ranking. h. Time of day on an analog watch - Interval scale because times are ordered with meaningful differences, but no absolute zero. i. Distance to the closest grocery store (miles) - Ratio scale as it has a true zero and measurable distances. j. Dates (1066, 1492, 1644, 1947, 1944) - Interval scale since differences are meaningful but no true zero date. k. Heights of women - Ratio scale due to true zero and meaningful numeric comparisons. l. Common letter grades (A, B, C, D, F) - Ordinal scale because they indicate a rank order.

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Key Concepts

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

Nominal Scale
Nominal scale is the most basic level of measurement. It categorizes data without assigning them an order or specific ranking. When utilizing the nominal scale, we observe how data fit into different categories without any inherent ranking or numeric value. For instance:
  • Colors of crayons - These fall into a nominal scale because each color is simply a category, and one color is not greater or lesser than another.
  • Social security numbers - These are used as unique identifiers, categorizing individuals without implying any order or hierarchy.
Nominal scales are helpful for categorizing data, but they do not allow for mathematical operations, such as addition or averaging.
Ordinal Scale
The ordinal scale goes a step further by introducing order into the data categories. Although the data can be ranked, the differences between the ranks are not meaningful or precisely measurable. Examples include:
  • High school soccer players classified by ability (Superior, Average, Above Average) - This is ordinal as it organizes players in order of ability.
  • Satisfaction survey with options like 'very satisfied', 'somewhat satisfied', 'not satisfied' - The scale reflects order of satisfaction.
While ordinal scales introduce ranking, they still don't measure the magnitude of difference between categories, so complex arithmetic operations are inappropriate.
Interval Scale
An interval scale not only involves ordered categories but also features meaningful, consistent intervals between values. However, this scale lacks a true zero, making the ratio between numbers less meaningful. Examples of interval scales include:
  • Baking temperatures - The difference between temperatures like 350掳F and 400掳F is meaningful, but there's no 'zero' temperature; zero degrees doesn't imply no temperature.
  • The time of day on an analog watch - Differences in time are consistent but lacking a true zero point, as time 0:00 doesn't represent the absence of time.
Measurements on an interval scale can be added or subtracted, but they cannot be multiplied or divided to produce valid results.
Ratio Scale
Ratio scale is the most advanced measurement level. It includes ordered categories, known intervals, and a meaningful zero, allowing for a wide range of mathematical operations, including ratios. This feature makes ratio scales widely applicable in data measurement. Consider these examples:
  • Incomes measured in dollars - There's a meaningful zero (no income), making comparisons such as twice as much income meaningful.
  • The heights of women - A natural zero exists, and you can compare heights and say one person is 1.5 times taller than another.
Ratio scales allow for both descriptive and inferential statistics, such as means, standard deviations, and variance, making them highly versatile in data analysis.

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Most popular questions from this chapter

Name the sampling method used in each of the following situations: a. A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport鈥檚 service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers who are sitting near gates and not taking naps while they wait. b. A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class. c. The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest. d. The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books. e. A political party wants to know the reaction of voters to a debate between the candidates. The after the debate, the party鈥檚 polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

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Identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data. Brand of toothpaste

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Seven hundred and seventy-one distance learning students at Long Beach City College responded to surveys in the 2010-11 academic year. Highlights of the summary report are listed in Table 1.39. $$\begin{array}{|l|l|}\hline \text { Have computer at home } & {96 \%} \\\ \hline \text { Unable to come to campus for classes } & {65 \%} \\ \hline \text { Age 41 or over } & {24 \%} \\ \hline \text { Would like LBCC to offer more DL courses } & {95 \%} \\ \hline \text { Took D L classes due to a disability } & {17 \%} \\ \hline \text { Live at least 16 miles from campus } & {13 \%} \\ \hline \text { TTook DL courses to fulfill transfer requirements } & {71 \%} \\ \hline\end{array}$$ Table 1.39 LBCC Distance Learning Survey Results a. What percent of the students surveyed do not have a computer at home? b. About how many students in the survey live at least 16 miles from campus? c. If the same survey were done at Great Basin College in Elko, Nevada, do you think the percentages would be the same? Why?
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