Question

identify the level of measurement of the data, and explain what is wrong with the given calculation.
in a survey, the political parties of respondents are identified as 1 for a democrat, 2 for a republican, 3 for a libertarian, and 4 for anything else. the average (mean) is calculated for 570 respondents and the result is 1.5.
the data are at the level of measurement.

Explanation:

The data (political parties labeled as 1, 2, 3, 4) are at the nominal level of measurement. Nominal data are used for categorization (like different political parties) and the numbers assigned are just labels. There is no inherent order or magnitude in a meaningful numerical sense for nominal data. Calculating a mean (which implies a numerical magnitude and arithmetic operations) is inappropriate for nominal - level data.

Answer:

The data are at the nominal level of measurement. It is wrong to calculate the mean for these data because nominal - level data are categorical (the numbers are just labels) and do not have a numerical value in the sense required for arithmetic operations like calculating a mean.