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.

Temperatures As this exercise is being written, it is 80oF at the author’s home and it is 40°F in Auckland, New Zealand, so it is twice as warm at the author’s home as it is in Auckland, New Zealand.

Short answer

The temperature measurement in degrees Fahrenheit follows the interval scale of measurement.

Ratios of values under the interval scale (double/half) have no meaning. Thus, it is wrong to say that it is twice as warm at the author’s home 80 degree F as in Auckland.

Step-by-step solution

Given information

The temperature at the author’s home is equal to 80 degrees Fahrenheit and the temperature in Auckland is equal to 40 degrees Fahrenheit.

Classification of data according to the level of measurement

Quantitative data is measured on the following two scales:

Interval: An interval level of measurement is used when a dataset consists of numerical values with a fixed gap between them. The true zero value does not exist. For example, SAT scores of an individual are measured on an interval scale.

Ratio: When a dataset consists of numerical values that have the exact distance between them each time and also an absolute zero value, a ratio scale is used. For example, the duration of working hours every day.

Multiplying or dividing values measured on the interval level is wrong as they do not hold relevant significance.

Identification of the appropriate scale

As temperature measured in degrees Fahrenheit is numerical and the difference between 40 and 45 degrees is equivalent to that of 75 and 80, so it is measured on the interval level.

Identification of the error in the given calculation

Since the true zero value of temperature measured in degrees Fahrenheit does not exist, ratios cannot be computed. Therefore, it is wrong to say that a place with 80 degrees Fahrenheit is twice as hotter as a place with 40 degrees Fahrenheit.