The below is question 2 from Study session 2, CFA Institute level 1 book. Though the book provided the answer, but it still does not make sense to me. Can someone please break it down for me?
State the type of scale used to measure the following sets of data: A. Sales in euros.
Answer: Ratio B. The investment style of mutual funds.
Answer: Nominal C. An analyst’s rating of a stock as underweight, market weight, or overweight, referring to the analyst’s suggested weighting of the stock in a portfolio.
Answer: Ordinal D. A measure of the risk of portfolios on a scale of whole numbers from 1 (very conservative) to 5 (very risky) where the difference between 1 and 2 represents the same increment in risk as the difference between 4 and 5.
Answer: Interval
(Institute 437) Institute, CFA. 2016 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. CFA Institute, 07/2015. VitalBook file.
Perhaps a firm understanding of the types of scales will help. Here goes:
Nominal : a list of names. The names distinguish the members of one group from those of another (e.g., bird, fish, reptile), but there is no sense of order (i.e., birds aren’t better or worse than fish; only different).
Ordinal : a list of (usually) numbers, used to rank members. The ranking tells which members are better than others (or worse than others), but there is no sense of magnitude (i.e., 2 is better than 1, and 3 is better than 2, and that’s all we know). The list may use words that aren’t numbers (e.g., good, average, poor, or buy, hold, sell) but the essential element is that they rank the items being classified.
Interval : a list of numbers for which the difference between numerical values corresponds to the degree of preference: not only is 3 better than 2, and 2 better than 1, but 3 is better than 2 _ by the same amount _ that 2 is better than 1. The main feature to remember about interval scales is that zero doesn’t mean “nothing”; it’s just another number on the scale. Temperature scales (e.g., Fahrenheit, Celsius) are typically interval scales: 0°F does not mean “no temperature”; it simply means a temperature that is one degree (Fahrenheit) lower than 1°F, and one degree (Fahrenheit) higher than −1°F.
Ratio : an interval scale for which zero means “nothing”. In addition to equal differences denoting the same amount of value ($11 − $10 is the same as $1,001 − $1,000), the ratios of numbers are meaningful: $2 is twice as good as $1, $2,000 dollars is twice as good as $1,000, and so on. Positive numbers are good, negative numbers bad, and zero is neutral.
Armed with this understanding, let’s look at the examples:
Sales in euro. This is clearly an interval scale (€11 − €10 is the same as €1,001 − €1,000), and €0 means “no sales”; this is a ratio scale.
Investment style of mutual funds. “Intermediate-term corporate bonds” is clearly different from “small-cap stocks”, but not necessarily better or worse; this is a nominal scale.
Analyst’s rating of “underweight”, “market weight”, and “overweight”. This ranks investments (i.e., “overweight” is better than “market weight”, and “market weight” is better than “underweight”), but there is no sense of how much better one is than another; this is a nominal scale.
Risk scale. Here they specify that it’s an interval scale, but we don’t even have a value of zero, so it can’t be a ratio scale; this is an interval scale.
