What are the characteristics of a population for which a mean/median/mode would be appropriate? Give some examples.

To understand when mean/median/mode are appropriate, we need the following definitions of level of measurement of data.

1) Nominal Scale

At the nominal scale (also called categorical scale), one uses labels. For example, if you do a survey, you are often asked to characterize things using “strongly disagree”, “disagree”, “neutral”, “agree”, “strongly agree”, this is an example of nominal scale. Another example would be a data set of majors of university students. In these data sets, only the mode is defined, thus only the mode is appropriate.

2) Ordinal Scale

At the ordinal scale, one uses rankings. For example, a class of students may be ranked by height, or the Mohs hardness scale (a scale that ranks the hardness of various metals/minerals from 1 being the …

This solution discusses the nominal sale, the ordinal scale, the interval scale and the ratio scale and how they relate to the appropriate statistical test in 556 words.