Question

In Exercises 29–32,identify the level of measurement of the data as nominal, ordinal, interval, or ratio. Also, explain what is wrong with the given calculation.

College Ranks As of this writing, U.S. News & World Report ranked national universities, including these results: Princeton (1), Harvard (2), Yale (3), and Columbia (4). The difference between Princeton and Harvard is the same as the difference between Yale and Columbia.

Short answer

The rankings of the four universities are measured on an ordinal scale.

Since the difference between the rankings is not exactly known, it is wrong to conclude that the difference between Princeton and Harvard is equal to the difference between Yale and Columbia.

Step-by-step solution

Given Information

The rankings of four national universities are given.

Identification of the appropriate scale

The levels of measurement explain the type of data at hand and what statistical techniques are suitable to apply. The ordinal level of measurement is explained below.

Ordinal: The ordinal scale is used to label variables that occur in order. The difference between the values cannot be quantified. For example, the temperature of a liquid can be classified as 1 for very hot, 2 for warm, 3 for cold, and 4 for very cold.

The four national universities are arranged in a particular order as per the U.S. News & World Report. It is known that rankings are measured on the ordinal scale. Thus, the appropriate scale of measurement is ordinal.

Identification of the error in the given calculation

It is inaccurate to conclude about the difference between any two values that are measured on the ordinal level as the difference between the values cannot be determined.

The difference among the ranks of the four universities is not measurable. Thus, it is wrong to say that the difference between the universities of Princeton and Harvard is equal to the difference between the universities of Yale and Columbia.