Identify the level of measurement of the data, and explain what is wrong with the given calculation.
In a survey, the hair colors of respondents are identified as 10 for brown hair, 20 for blond hair, 30 for black hair, and 40 for anything else. The average (mean) is calculated for 594 respondents and the result is 22.3.
What is wrong with the given calculation?
A. Such data are not counts or measures ofanything, so the average (mean) needs to be computed in a different way.
B. The true average (mean) is 19.5.
C. Such data are not counts or measures.of anything, so it makes no sense to compute their average (mean).
D. There is nothing wrong with the given calculation.
Answer:
This type of data are not measurement of
anything, so it is not feasible to calculate
their average(Mean)
The level of measurement of the data in this case is nominal, as the numbers assigned to hair colors (10, 20, 30, 40) are arbitrary categories without any inherent order or numerical value.
The correct answer is C. The calculation is incorrect because computing the average (mean) for nominal data, which are not counts or measurements of any quantitative variable, does not make sense. The numbers assigned to the hair colors are merely labels or categories and do not represent any meaningful numerical values. Therefore, finding the average of these arbitrary numbers is not meaningful or valid.
To calculate the average (mean) of nominal data, you would need to convert the data into a different measurement level, such as ordinal (if there is a meaningful order to the categories), interval, or ratio (if there is a meaningful numerical relationship between the categories). In this case, it would be more appropriate to analyze the distribution of the hair colors using frequencies or percentages rather than calculating an average.