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.
Social Security Numbers As part of a project in a statistics class, students report the last four digits of their Social Security numbers, and the average (mean) of those digits is computed to be 4.7.

검증된 단계별 안내

Identify the level of measurement: Social Security numbers are identifiers and do not have a meaningful order or zero point. Therefore, they are measured at the nominal level.

Explain the nominal level: The nominal level of measurement is used for data that are categories without any intrinsic ordering. Examples include names, labels, or categories.

Discuss the inappropriateness of the calculation: Since Social Security numbers are nominal data, it is inappropriate to perform arithmetic operations such as calculating the mean.

Clarify why the mean is inappropriate: The mean is a measure of central tendency that requires interval or ratio level data, where the numbers have meaningful differences and a true zero point.

Conclude with the correct approach: For nominal data like Social Security numbers, appropriate analyses might include counting frequencies or identifying modes, but not calculating means.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Levels of Measurement

Levels of measurement refer to the different ways data can be categorized, which include nominal, ordinal, interval, and ratio. Nominal data are labels without any quantitative value, ordinal data have a meaningful order but no consistent difference between values, interval data have consistent differences but no true zero, and ratio data have both consistent differences and a true zero, allowing for meaningful ratios.

Nominal Data

Nominal data are used for labeling variables without any quantitative value. In the context of Social Security numbers, these numbers serve as identifiers and do not have any inherent numerical value or order. Therefore, they are considered nominal data, which means calculating a mean or average is not meaningful or appropriate.

Inappropriate Calculations with Nominal Data

Calculating the mean of nominal data is inappropriate because nominal data are categorical and do not possess numerical properties that allow for arithmetic operations. Social Security numbers are identifiers, and averaging them does not yield a meaningful result, as they do not represent quantities or measurements that can be averaged.