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 1.2.21
Textbook Question
In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.
College Students In order to better plan for the incoming freshman class, a college dean asks each newly admitted student to identify their likely major (physics, business, math, psychology, engineering, law, etc.).

1
Understand the four levels of measurement: Nominal, Ordinal, Interval, and Ratio. Nominal involves categories without a specific order, Ordinal involves categories with a specific order, Interval involves numerical scales with equal intervals but no true zero, and Ratio involves numerical scales with a true zero.
Identify the type of data being collected. In this case, the data consists of categories of college majors such as physics, business, math, etc.
Determine if there is any inherent order to the categories. College majors do not have a natural order; one major is not inherently 'higher' or 'lower' than another.
Since the data consists of categories without a specific order, it fits the definition of the nominal level of measurement.
Conclude that the level of measurement for the given data (college majors) is nominal, as it involves categorizing students into groups without any ranking or order.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Levels of Measurement
The levels of measurement refer to the different ways data can be categorized and quantified. They include nominal, ordinal, interval, and ratio scales. Each level has distinct characteristics that determine how data can be analyzed and interpreted, influencing the types of statistical tests that can be applied.
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Nominal Scale
The nominal scale is the simplest level of measurement, used for categorizing data without any order or ranking. In this scale, data is classified into distinct categories that are mutually exclusive, such as names of majors (e.g., physics, business). The only permissible operation is counting the frequency of each category.
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Ordinal Scale
The ordinal scale involves categorizing data into ordered categories, where the order matters but the differences between the categories are not quantifiable. For example, if students were ranked by their preference for majors, the order would indicate preference but not the degree of difference between them. This scale allows for comparisons in terms of greater or lesser but not precise measurements.
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