Ch. 1 - Introduction to Statistics

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 1 - Introduction to Statistics

Problem 1.2.34

Chapter 1, Problem 1.2.34

Directions in Degrees Standard navigation systems used for aviation and boating are based on directions measured in degrees, with north represented by 0° Relative to north, east is 90°, south is 180°, and west is 270°. What is the level of measurement of such directions measured in degrees?

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Identify the four levels of measurement in statistics: nominal, ordinal, interval, and ratio.

Consider the characteristics of the interval level of measurement: it has meaningful differences between values, but no true zero point.

Recognize that directions in degrees have meaningful differences (e.g., the difference between 90° and 180° is 90°), but there is no true zero point because 0° is arbitrary and represents north.

Understand that directions measured in degrees can be added and subtracted, which is a property of interval data.

Conclude that the level of measurement for directions in degrees is interval, as it meets the criteria of having meaningful differences without a true zero point.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Levels of Measurement

Levels of measurement refer to the nature of data and dictate the types of statistical analyses that can be performed. The four levels are nominal, ordinal, interval, and ratio. Each level has specific characteristics, such as the presence of a true zero or the ability to rank data, which determine how data can be interpreted and manipulated.

Interval Scale

An interval scale is a level of measurement where the difference between values is meaningful, but there is no true zero point. This means that while you can add and subtract values, you cannot meaningfully multiply or divide them. Examples include temperature in Celsius or Fahrenheit and directions in degrees, where the zero point is arbitrary.

Circular Data

Circular data involves measurements that wrap around, such as angles or time on a clock. In these cases, the data is cyclical, meaning that the end of the scale connects back to the beginning. This requires special consideration in analysis, as traditional linear methods may not apply, and the data is often treated using techniques specific to circular statistics.

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Related Practice

Textbook Question

In Exercises 21–28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study.

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Textbook Question

In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)

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Context of the Data Refer to the table of body temperatures. Is there some meaningful way in which each body temperature recorded at 8 AM is matched with the 12 AM temperature?

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Textbook Question

In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.

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Textbook Question

In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)

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Conclusion If we analyze the listed body temperatures with suitable methods of statistics, we conclude that when the differences are found between the 8 AM body temperatures and the 12 AM body temperatures, there is a 64% chance that the differences can be explained by random results obtained from populations that have the same 8 AM and 12 AM body temperatures. What should we conclude about the statistical significance of those differences?

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