Question

The following data are derived from which measurement scale? a. My happiness score on a scale of 1 to \(10=7\) b. My weight \(=192\) lbs. c. The city I live in = Culver City d. My current body temperature \(=99.8\) ?F e. The number of cheeseburgers I can eat before passing out \(=12\) f. My license plate number = \(1 \mathrm{LUVG} 1 \mathrm{~S}\)

Short answer

a. Ordinal, b. Ratio, c. Nominal, d. Interval, e. Ratio, f. Nominal

Step-by-step solution

- Understand the types of measurement scales

There are four primary types of measurement scales: Nominal, Ordinal, Interval, and Ratio.- Nominal scales classify data into distinct categories without any order (e.g., license plate numbers).- Ordinal scales classify data into categories that have a meaningful order, but the differences between categories are not uniform (e.g., happiness scores).- Interval scales have ordered categories and the differences between categories are equal, but there is no true zero (e.g., body temperature in Fahrenheit).- Ratio scales have all the properties of interval scales, and also have a meaningful zero point (e.g., weight).

- Analyze happiness score

a. My happiness score on a scale of 1 to 10. This is an ordinal scale because it ranks the level of happiness, but the differences between the scores are not uniformly interpretable.

- Analyze weight

b. My weight = 192 lbs. Weight is measured on a ratio scale because it has a meaningful zero and equal intervals between measurements.

- Analyze city of residence

c. The city I live in = Culver City. The name of the city is nominal data because it categorizes and labels without any quantitative value or order.

- Analyze body temperature

d. My current body temperature = 99.8°F. Body temperature is measured on an interval scale because it has equal intervals, but there is no true zero point (a body temperature of 0°F does not indicate absence of heat).

- Analyze number of cheeseburgers

e. The number of cheeseburgers I can eat before passing out = 12. This is a ratio scale because it has a true zero (eating 0 cheeseburgers) and equal intervals between the numbers.

- Analyze license plate number

f. My license plate number = 1LUVG1S. License plate numbers are nominal data because they are used to categorize and label vehicles without any numerical or order significance.

Key concepts

Nominal Data

Nominal data is used for labeling variables without any quantitative value or order. It is simply about categorizing and naming data. An example from the exercise is the city you live in, like Culver City. This doesn't imply any sort of hierarchy or numerical significance. Another example is your license plate number, which also does not denote any order or value, just a unique identifier for your vehicle.

• Nominal data doesn't imply any specific order
• Used only for categorizing or labeling
• Examples: City names, license plate numbers, types of fruits

Ordinal Data

Ordinal data deals with order or rank among variables. Think of it as placing items in a queue where the order matters but the intervals between them don't have to be equal or described. From the exercise, a happiness score on a scale of 1 to 10 is an example. Although a score of 7 is higher than 5, it doesn’t necessarily mean the degree of happiness is proportionally higher. It signifies rank without proportion.

• Data has meaningful order
• Differences between ranks are not uniform
• Examples: Happiness scales, grades in school (A, B, C), class ranks

Interval Scale

Interval scales provide not just order but also consistent differences between values. It is important to note that interval scales have equal intervals but lack a true zero point. Body temperature in Fahrenheit, like 99.8°F from the exercise, is a great example. You can determine the difference between values (01°F), but a temperature of 0°F does not mean 'no temperature'.

• Equal intervals between values
• No true zero point
• Examples: Temperature in Celsius or Fahrenheit, calendar years, time on a clock

Ratio Scale

A ratio scale has all the features of an interval scale, plus a true zero point, meaning 'none' or 'an absence of' the variable measured. Measurements like weight, height, or number of cheeseburgers you can eat are good examples. In the exercise, weight measured in pounds and the number of cheeseburgers (e.g., 12) are both ratio scales. Zero means you have no weight or you ate zero cheeseburgers.

• Equal intervals between values
• Has a true zero point
• Examples: Weight, height, age, number of items