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Ch. 2 - Exploring Data with Tables and Graphs
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 2 - Exploring Data with Tables and GraphsProblem 2.CRE.4c
Chapter 2, Problem 2.CRE.4c

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B
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Data Type


c. Identify the level of measurement of the listed earthquake depths: nominal, ordinal, interval, or ratio.

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Step 1: Understand the levels of measurement. There are four levels: nominal (categorical data with no order), ordinal (categorical data with a meaningful order but no consistent difference between values), interval (numerical data with consistent differences but no true zero), and ratio (numerical data with consistent differences and a true zero).
Step 2: Analyze the nature of the earthquake depths. Depths are numerical values that represent a measurable quantity (distance in kilometers).
Step 3: Determine if the data has a true zero point. Since a depth of 0 km is meaningful and indicates no depth, the data has a true zero point.
Step 4: Check if the differences between values are consistent. For example, the difference between 10 km and 20 km is the same as the difference between 30 km and 40 km, which confirms consistent differences.
Step 5: Conclude that the level of measurement for earthquake depths is 'ratio' because the data is numerical, has consistent differences, and includes 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 different ways in which variables can be categorized and quantified. The four primary levels are nominal, ordinal, interval, and ratio. Each level has distinct characteristics, with nominal being the simplest (categorical data) and ratio being the most complex (includes a true zero point). Understanding these levels is crucial for determining appropriate statistical analyses.
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Ratio Level of Measurement

The ratio level of measurement is characterized by the presence of a true zero point, allowing for the comparison of absolute magnitudes. In this level, both differences and ratios between values are meaningful. For example, in measuring earthquake depths, a depth of 0 km indicates the absence of depth, making it a ratio measurement, as one can say that a depth of 10 km is twice as deep as 5 km.
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Richter Scale

The Richter scale is a logarithmic scale used to measure the magnitude of earthquakes. It quantifies the energy released at the source of the earthquake, with each whole number increase on the scale representing a tenfold increase in measured amplitude and approximately 31.6 times more energy release. Understanding the Richter scale is essential for interpreting earthquake data, including magnitudes and their implications for depth measurements.
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Related Practice
Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

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Data Type


a. The listed earthquake depths (km) are all rounded to one decimal place. Before rounding, are the exact depths discrete data or continuous data?

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Textbook Question

Normal Distribution If the following data are randomly selected, which are expected to have a normal distribution?


d. Exact volumes of Coke in 12 oz cans

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Textbook Question

It’s Like Time to Do This Exercise In a Marist survey of adults, these are the words or phrases that subjects find most annoying in conversation (along with their frequencies of response): like (127); just sayin’ (81); you know (104); whatever (219); obviously (35). Construct a pie chart. Identify one disadvantage of a pie chart.

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Textbook Question

Whatever Use the same data from Exercise 7 to construct a Pareto chart. Which graph does a better job of illustrating the data: Pareto chart or pie chart?

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Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

[Image]

Data Type


b. For the listed earthquake depths, are the data categorical or quantitative?

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Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

[Image]

Data Type


d. Given that the listed earthquake depths are part of a larger collection of depths, do the data constitute a sample or a population?

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