1. Intro to Stats and Collecting Data
Intro to Stats
1:58 minutesProblem 2.CRE.4a
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?
Verified step by step guidance1
Understand the difference between discrete and continuous data: Discrete data consists of distinct, separate values (e.g., counts like 1, 2, 3), while continuous data can take any value within a range (e.g., measurements like 1.1, 1.2, 1.3).
Examine the context of the problem: Earthquake depths are measured in kilometers and rounded to one decimal place. This suggests that the original data is based on measurements.
Recognize that measurements, such as depth, are typically continuous because they can take any value within a range, even if they are later rounded.
Consider the rounding process: Rounding does not change the nature of the original data. Even though the depths are rounded to one decimal place, the exact (pre-rounded) depths could still take any value within a range.
Conclude that the exact (pre-rounded) earthquake depths are continuous data because they represent measurements that can take any value within a range, not distinct, separate values.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Discrete vs. Continuous Data
Discrete data consists of distinct, separate values, often counted in whole numbers, such as the number of students in a class. In contrast, continuous data can take any value within a given range and is often measured, such as the depth of an earthquake, which can include fractions and decimals.
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Measurement Scales
Measurement scales categorize data into different types, including nominal, ordinal, interval, and ratio scales. Earthquake depths are typically measured on a ratio scale, which has a true zero point and allows for meaningful comparisons and calculations, such as determining how much deeper one earthquake is than another.
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Rounding in Data
Rounding is the process of reducing the number of digits in a number while maintaining its value as close as possible to the original. When data is rounded, it can affect the classification of the data type; however, the underlying nature of the data (discrete or continuous) remains unchanged, as it is based on the original measurements before rounding.
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