Ch. 1 - Introduction to Statistics

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 1 - Introduction to Statistics

Problem 1.2.30

Chapter 1, Problem 1.2.30

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.

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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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Textbook Question

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Textbook Question

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Textbook Question

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