Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
1. Intro to Stats and Collecting Data
Intro to Stats
Problem 1.2.34
Textbook Question
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?

1
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.
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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.
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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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